Light

Convex mirror forms the smaller image but it can show a larger view area. So, it is used by vehicles as a ‘rear-view mirror’ and as a side mirror. They are also fitted in ATM’s for security purpose so that customer can see the back view.

Refractive Index is the ratio of the velocity of light in a vacuum to its velocity in a specified medium. Since the refractive index is greater than equal to 1. Hence, the velocity of light is maximum in a vacuum.

When light travels from one medium to another at the interface the light changes its direction or light bends. This effect is known as Refraction. When light travels from rarer medium to denser medium, the light bends towards the normal and this causes object to appear nearer than they are.

Focal length of a convex mirror is always positive.

Using our sign convention, in a convex mirror when we move from pole towards the center of the hemisphere, the distance is + ve. Hence, the focal length is positive.

According to the definition, the focal length is half the distance from the pole of the mirror to the center of the sphere. In the case of a plane mirror, the radius of the imaginary sphere is infinity, so the focal length is also infinity.

In the convex mirror, the image is always formed behind the mirror so the image will always be virtual, moreover the image is always on the same side of the axis, so always erect.

Power is defined as inverse of focal length (in meters).

Hence, f = 0.5 m

In hypermetropia or far sightedness a person is able to see the distant objects clearly but cannot see nearby objects distinctly.

When we keep the object at 2F, we get a real & Inverted image of the same size as an object at 2F (another side of the lens).

When we keep an object at infinity, we get a virtual, erect and diminished image of the object at the focus.

If any object absorbs all colors of light, then it is visible black. The color we see by any object is the color which the object reflects.

If the height of a person is height , then to view the full image of himself from head to toe the mirror should be at least of height.

Derivation

Consider a person AB, such that A represents the highest point on the head, B, the lowest point on foot and E is the fixed eye level. The person will be able to see every part of his body if he can see points A and B. Let MN be the minimum length of mirror fixed on the wall, such that rays AM and BN, after reflection, reach the eye of a person, thereby forming image A₁B₁, when produced backward.

In ΔAEA₁, CM is parallel to AE and C is the mid-point of AA₁.
M is the mid-point of A₁E.
Similarly, in Δ BEB₁ ND is parallel to BE and D is the mid-point of BB₁,
N is the mid-point of B₁E.
Now in Δ A₁B₁E, M is the mid-point of A₁E and N is the mid-point of B₁E.
MN is parallel to and half of A₁B₁.
But A₁B₁ = AB
MN = AB
Thus in order to see the full length of a person, requires a plane mirror, which is half of its own height. This relation is true for any distance of the object from a plane mirror.

Consider the following diagram

The above diagram represents a ray which is falling at an angle of 30° to the plane mirror.

Using Law of reflection, the reflected will be at an angle of 60° from the normal to the plane mirror.

The angle between incident ray and the reflected ray will be 120°.

● It is used in vehicles as a rear-view mirror & side mirror.

● In today’s time, it is fitted in ATM’s for security purpose so that customer can see the back view.

● They are put on the corners of roads so that you can see any cars coming to avoid the collisions.

● The satellite disc in our house that is a concave mirror which collects signal from the satellite and passes them to the receiver.

● The concave mirror is also used in the telescope in which the rays from Sun, Moon and other heavenly bodies are these parallel rays’ forms image on the focus.

● In daily life, it is used as a shaving mirror.

In a spherical mirror

1. The distance from pole to object is represented by ‘u’.

2. The distance from pole to the image is represented by ‘v’.

3. The distance from pole to focus is represented by ‘f’.

These three quantities are related by an equation known as Mirror Equation which is given below

Snell's is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.

Snell's law states that the ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of phase velocities in the two media, or equivalent to the reciprocal of the ratio of the indices of refraction.

‘v’ is object distance

‘u’ is image distance

’f’ is the focal length

Since parallel rays are falling on the convex lens, hence the object is at infinity. So, the image will be formed at the focus.

S.I. unit of power of the lens is diopter, and

1 diopter

A person suffering from myopia can see near by objects clearly but cannot see distant objects distinctly. A person with this defect has the far point nearer than infinity. In a myopic eye, the image of a distant object is formed in front of the retina.

The following eye defect can be corrected by using the lens of appropriate power:-

● Myopia – by using the concave lens of suitable power.

● Hypermetropia – by using a convex lens of appropriate power.

● Presbyopia – using the bifocal lens.

● Astigmatism – using the cylindrical lens.

With the aging the transparency and elasticity of the lens gradually decrease. The crystalline lens of people of old age becomes milky and cloudy. Due to this reason, it starts reflection and objects seems cloudy. This condition is called a cataract.
The image is given here:

The image which is visible to us in the shaving mirror is real and inverted.

When we look into the mirror, we are farther than the focal length of the mirror, thus our eyes try to image the real image formed by the mirror on the mirror itself. Thus, we just assume that the image is formed on the mirror, but that is not true for that case if we bring our eye very close to the mirror we would no longer see the image on the mirror because the image is now virtual.

When light falls on a highly polished surface such as a mirror, reflects most of the light rays falling on it. The plane surface seems shiny from a certain direction. If we change the direction of mirror the mirror shines from another direction. When light beam falls on a shiny surface they bounce back into the same medium in a certain direction, this phenomenon is called regular reflection.

When light falls on rough surfaces, dust & smoke, the light is reflected and spread in every direction. The phenomenon of spreading light in all directions by the rough surfaces is called diffused reflection.

The phenomenon due to which the left-hand side of an object appears as the right-hand side of the object and vice versa is called a lateral inversion.

For example, the word AMBULANCE is painted left-right inverted on the ambulance so that when the driver of a vehicle in front looks into his rear-view mirror, he can make out the word AMBULANCE quickly and give way.

The sign conventions are as follows: -

● The object is placed always to the left of the mirror. This implies that the light from the object falls on the mirror from the left-hand side.

● All the distances parallel to the principal axis are measured from the pole of the mirror.

● All the distances measured to the right of the origin (along with + ve x-axis) are taken as positive while those measured to the left of the origin (along -ve x-axis) are taken as negative

● Distance measured perpendicular along + ve y-axis is taken as positive while those measured along -ve y-axis is taken as negative.

When light travels from one medium to another at the interface the light changes its direction or light bends. This effect is known as Refraction. When light travels from rarer medium to denser medium, the light bends towards the normal and this causes the object to appear nearer than they are.

The laws of refraction

● The incident ray reflected ray, refracted ray and the normal of the system lie in the same plane.

● The incident ray, coming from one medium to the boundary of another medium, is refracted by a rule derived from a physicist Willebrord Snellius. He found that there is a constant relation between the angle of the incident ray and angle of refracted ray. This constant is the refractive index of the second medium relative to the first medium.

The various types of lens are as follows: -

● Double Convex Lens – The both surfaces of the lens are convex.

● Plano-Convex Lens – Its one surface is convex and other is plane.

● Concavo-Convex – Its one surface is convex and other is concave.

● Double concave lens – This type of lens has both concave surfaces.

● Plano concave lens – This has one surface as concave and other is a plane.

● Convexo-Concave Lens – One surface of the lens is convex and another surface is concave.

I. Principal axis – The straight line which joins the center of curvature.

II. Optical Center – The center of a lens is its optical center. A ray of light through the optical center of a lens passes without suffering any derivation.

I. The radius of curvature – The radius of the curve surfaces of the lens is called radius of curvature.

II. Center of curvature – The curved surfaces of the lens is considered as a part of the hollow sphere of glass. The center of these spheres is called center of curvature.

● The rays parallel to principal axis passes from principal focus after refraction. When this parallel incident ray falls on the concave lens they diverge back after refraction. When they are extended backward they seem to be meeting at focus.

● A ray of light passing through a principal focus after refraction from a convex lens will emerge parallel to the principal axis. A ray of light appearing to meet at the principal focus of a concave lens, after the refraction will emerge parallel to the principal axis.

● A ray of light passing through the optical center of a lens will emerge without any deviation.

I. Object at infinity –

II. Object at limited distance

The ability of a lens to converge or diverge the light rays is known as power of lens. A convex lens of short focal length bends the light rays through large angles, by focusing them closer to the optical center. Opposite to this convex lens of more focal length bend the light rays through short angle. Concave lens of very short focal length causes high divergence than with the long focal length lens.

Numerically, Power of lens is inversely proportional to focal length which is in meters.

A person with myopia can see nearby objects clearly but cannot see distant objects distinctly. A person with this defect has the far point nearer than infinity. In a myopic eye, the image of a distant object is formed in front of the retina.

Causes of defect

● Excessive curvature of eye lens

● Elongation of eye-ball

Correction of defect

This defect can be corrected by using concave lens of suitable power. A concave lens of suitable power will bring the image back on the retina.

In hypermetropia person Is able to see distant objects clearly but cannot see nearby objects distinctly. The near point for the person is farther away from the normal near point (25cms).

Cause of defect

● The focal length of the eye is too long

● The eye ball has become too small

Correction of defect

This defect can be corrected by using a convex lens of appropriate power.

● Presbyopia – The power of accommodation of eye usually decrease with ageing. For most of the people, the near point gradually recedes away. They find it difficult to see nearby objects comfortably and distant objects also.

● Astigmatism - It takes place due to irregular curvature or spherical shape of the cornea. In this defect, person is not able to differentiate between vertical and horizontal lines at a time. It can be corrected using the cylindrical lens.

The process by which the ciliary muscles change the focal length of an eye lens to focus distant or near objects clearly on the retina is called the accommodation of the eye.

Power of Accommodation = (since f = 0.25 m for normal human eye)

Power = 4D

The range of vision of the normal human eye is from infinity to about 25cms.

The following ray diagram is applicable to the above question

a) The image is formed between F and C.

b) Size of the image is less as compared to the size of the object.

c) The image is real and inverted.

a) The image is formed at C.

b) Size of the image is equal to the size of the object.

c) The image is real and inverted.

a) The image is formed beyond C.

b) Size of the image is enlarged.

c) The image is real and inverted.

a) The image is formed at infinity

b) Size of image is highly enlarged

c) The image is real and inverted.

a) The image is formed behind the mirror.

b) Size of image is enlarged

c) The image is virtual and erect

When light travels from one medium to another at the interface the light changes its direction or light bends. This effect is known as Refraction. When light travels from rarer medium to denser medium, the light bends towards the normal and this causes the object to appear nearer than they are.

The laws of refraction

● The incident ray reflected ray, refracted ray and the normal of the system lie in the same plane.

● The incident ray, coming from one medium to the boundary of another medium, is refracted by a rule derived from a physicist Willebrord Snellius. He found that there is a constant relation between the angle of the incident ray and angle of refracted ray. This constant is the refractive index of the second medium relative to the first medium.

An experiment can be done with a glass slab to understand the incident of refraction easily.

Experiment - Fix a sheet of white paper on a drawing board using drawing pins. Place a rectangular glass slab over the white sheet in the middle of the sheet. Draw the outline of the slab with a pencil. Name the outline ABCD. The points O and O’ lie on surfaces separating two transparent media. Draw a perpendicular NN’ to AB at O and another perpendicular MM’ to CD at O’. The light ray at point O has entered from a rarer medium to a denser medium, that is, from air to glass. Note that the light ray has bent towards the normal. At O’, the light ray has entered from glass to air, that is from a denser to a rarer medium. The light here has bent away from the normal.

You may observe that the emergent ray is parallel to the direction of the incident ray.

● Concave mirror

a) The image is formed at the focus.

b) It is real and inverted.

c) It is highly diminished.

● Convex mirror

a) The image is formed at the focus, behind the mirror.

b) It is virtual, erect and diminished.

● Convex Lens

a) The image is formed at second principal focus F₂

b) It is diminished, real and inverted.

● Concave Lens

a) The image is formed at F₁.

b) It is highly diminished, virtual and erect.

● Concave mirror

● Convex Mirror

● Convex Lens

● Concave Lens

(i)

(ii)

(iii)

between focus and optical centre.

A) Image is formed beyond 2F₂

B) It is larger in size than object

C) It is real, inverted.

at focus

A) Image is formed at infinity.

B) It is highly magnified, real and inverted.

between focus F₁ and 2F₁

a) Image is formed beyond 2F₂

b) It is larger in size than object

c) It is real, inverted.

at 2F₁

a) Image is formed at 2F₂

b) Image is of same size as that of object

c) It is real and inverted.

between 2F₁ & infinity

a) Image is formed between F₂ and 2F₂.

b) It is diminished, real and inverted.

Explain the eye defects in detail along with the method to correct them.

● Myopia –

A person with myopia can see near by objects clearly but cannot see distant objects distinctly. A person with this defect has the far point nearer than infinity. In a myopic eye , the image of a distant object is formed in front of the retina.

Causes of defect

● Excessive curvature of eye lens

● Elongation of eye-ball

Correction of defect

This defect can be corrected by using concave lens of suitable power. A concave lens of suitable power will bring the image back on the retina.

● Hypermetropia

In hypermetropia person Is able to see distant objects clearly but cannot see nearby objects distinctly. The near point for the person is farther away from the normal near point (25cms).

Cause of defect

● The focal length of eye is too long

● The eye ball has become too small

Correction of defect

This defect can be corrected by using a convex lens of appropriate power.

● Presbyopia

The power of accommodation of eye usually decreases with aging. For most of the people, the near point gradually recedes away. They find it difficult to see nearby objects comfortably and distant objects also. This defect can be corrected using Bifocal Lens.

● Astigmatism

It takes place due to irregular curvature or spherical shape of the cornea. In this defect, person is not able to differentiate between vertical and horizontal lines at a time. It can be corrected using the cylindrical lens.

● Cataract

With ageing, the transparency and elasticity of lens gradually decrease. The crystalline lens of people of old age becomes milky and cloudy. Due to this reason, it starts reflection and objects seems cloudy. This condition is called Cataract. This can be corrected using minor surgical operation.

Given

The distance of the object from the mirror (u) = - 40cm (as the object is on the left side of mirror and acc. To our sign convention)

The focal length of the mirror (f) = -30 cm (Focal length is negative in case of the concave mirror.)

Image distance (v) = ?

Magnification (m) = ?

Formula Used

Using mirror formula

V = -120 (same side of mirror)

The image is real.

Magnification = = -3

Hence, the image is 3 times the object and image is inverted.

Given

Focal length of convex mirror = +16cm (focal length of convex mirror is positive)

The distance of image = + 8cm (Since in case of a convex mirror, the image is always virtual)

The distance of Object = ?

Formula Used

Using the above formula

U = -16 cm

Hence, the object is placed at a distance of 16cm in front of the mirror.

Given

The distance of object from the lens = - 60 cms (since the object is on the left-hand side of lens and acc. To our sign convention)

The focal length of the convex lens = +30 cms ( focal length of convex length is positive.)

Height of object = 3 cm

Formula Used

Lens Formula

Magnification formula

Using lens formula

V = + 60 cms

Hence the image is at a distance of 60 cms from the lens and the image is real.

Using magnification formula

M =

M = -1

Hence, the image is of the same size as that of object and the image is inverted.

Given

The distance of object from lens = -10cm (since the object is on the left-hand side of lens and acc. To our sign convention)

Focal length of convex lens = + 40cm (focal length of convex length is positive)

The distance of image from Lens = ?

Formula Used

Lens Formula

Magnification formula

Using lens formula

V = = -13.33cm

Hence, the image is on the same side of object at the distance of 13.33 cm from lens and the image is virtual.

Using magnification formula

M = 1.33

The image is 1.33 times the object and is erect.

Given

Focal length of Concave mirror = -30cm (focal length of concave mirror is negative)

Distance of object from mirror = -20 cm (since object is on the left-hand side of lens and acc. To our sign convention)

Distance of image from mirror = ?

Formula Used

Mirror formula

Magnification formula

Using Mirror formula

V = 60 cm

Hence the image is at a distance of 60cm from mirror and is virtual.

Using magnification formula

M = 3

Hence, the image is 3 times the object and is erect.

Given

Distance of image from concave lens = -10cm (as in case of concave lens, image is always virtual)

Focal length of concave lens = -15cm (focal length of concave lens is always negative)

Formula used

Lens Formula

Using lens formula

U = -30cm

The distance of object from the lens is 30cm

Given

Focal length of convex lens = + 10cm (focal length of convex lens is always positive)

Since nearest distance of vision is 25cm

Formula Used

Lens Formula

Magnification formula

Now let’s re-write the above formula

Using mirror equation

Now replacing the ‘u’ in magnification equation with the above u we get

Now, according to our sign convention v is negative and equal to D (nearest distance of vision)

Hence the equation becomes

Putting the values, we get

M = 3.5