Light – Reflection And Refraction

All the light rays which are travelling parallel to the principal axis are bound to meet at a point on the principal axis after reflection from the mirror. This point on the principal axis is called the principal focus of the mirror.

Concave mirror produces an erect and enlarged image of an object.

We prefer a convex mirror as a rear-view mirror in vehicles because of the following reasons:

(i) A convex mirror always produces an erect image of the objects.

(ii) Also, the image formed is diminished due to which the convex mirror gives a wider view. Therefore, rear-view mirrors are made of convex mirrors.

R=+32cm and f=R2=+322=+16cmR=+32cm and f=R2=+322=+16cm

Thus, the focal length of convex mirror is 16 cm

In this problem we are given,

Magnification, m = -3 (Image is real)

Object distance, u = -10 cm (To the left of mirror)

Image distance, v = ? (To be calculated)

Putting these values in the magnification formula for a mirror:

Thus, the image is located at a distance of 30 cm in front of the mirror on its left side.

When a ray of light travelling in air enters obliquely into water, it bends towards the normal. This is because water has high refractive index which makes it optically denser than air. Thus, the light ray bends towards the normal when it enters water.

We know that:

Refractive index of glass = (Speed of light in air (or vacuum))/(Speed of light in glass)

1.50 = (3×10⁸)/(Speed of light in glass)

Or, Speed of light in glass = = 2×10⁸ ms^-1

Thus, the speed of light in glass is 2×10⁸ ms^-1 (or 2×10⁸ m/s).

(a) The medium having highest refractive index has the highest optical density. Since diamond has highest refractive index of 2.42 Thus, diamond has the highest optical density.

(b) The medium having lowest refractive index has the lowest optical density. Since air has the lowest refractive index of 1.0003 Thus, air has the lowest optical density.

The light travels fastest in that medium which has the lowest refractive index i.e. lowest optical density. In the medium having lowest refractive index, the speed of light rays is high. From the three materials given, kerosene, turpentine and water, water has the lowest refractive index (of 1.33), so light travels fastest in water.

By saying that the refractive index of diamond is 2.42, we mean that the ratio of speed of light in air (or vacuum) to the speed of light in diamond is equal to 2.42.

1 Dioptre is the power of a lens whose focal length is 1m.

i.e.

(i) In this case needle is the object. Since the image is real, inverted and of same size as the needle (or object), the needle must be at the same distance (50 cm) in front of lens, as the image is behind the lens. Thus, the needle is placed at a distance of 50 cm from lens in the front.

(ii) When the image formed by a convex lens is of the same size as the needle (or object), then the distance of needle from the lens is 2f (twice the focal length).

In this case: focal length, f = 50/2cm

Thus, the focal length of this convex lens is +25 cm. This is equal to (+25)/100m or +0.25m. Now, Power, P= 1/(f(in meters)) = 1/(+0.25) = +4.0 D

So, the power of this convex lens is +4.0 diopters.

The focal length of a concave lens is considered negative and hence written with a minus sign. So, focal length of concave lens, f = -2 m

Now, Power, P =

Clay cannot be used to make a lens. Because it is opaque material, and light cannot pass through it.

When the image formed by a concave mirror is observed to be virtual, erect and larger than the object, the position of image will be between the pole of the mirror and its principal focus

The object should be placed at twice the focal length to get a real image of the size of the object. Thus, option (b) is correct.

A spherical mirror and a thin spherical lens each having a focal length of -15 cm are both concave.

Plane mirror or convex mirror both form erect images. Thus, option (d) is correct.

A convex lens of focal length 5 cm is used for reading small letters. Thus, option (c) is correct.

In order to obtain an erect image of an object with a concave mirror, the object should be at a distance less than its focal length as seen below:

Here the focal length of concave mirror is 15 cm. So to obtain an erect image the object by using this concave mirror, the object should be placed at any distance which is less than 15 cm from the mirror. The nature of image will be virtual. The image will be larger than the object.

(a) A concave mirror is used in the headlights of a car. This is because when, a lit bulb is placed at the focus of the concave reflector, then the concave reflector produces a powerful beam of parallel light rays. This beam of light helps us to see things up to a considerable distance in the darkness of night.

(b) A convex mirror is used as side-view mirror or rear-view mirror in a vehicle. This is because:

(i) A convex mirror always produces an erect image of the objects

(ii) the image formed in a convex mirror is highly diminished due to which a convex mirror gives a wide field of view of the traffic.

(c) A concave mirror is used in a solar furnace. This is because when the solar furnace is placed at the focus of a large concave reflector, then the concave reflector converges and focuses the sun's heat rays on the furnace due to which the solar furnace gets very hot.

When a convex lens is half covered with a black paper. It will produce a complete image of an object because light rays can still pass through its optical centre (as shown in figure given here).

A converging lens means a convex lens. The diagram is shown below:

Here, Object distance, u = - 25 cm

Image distance, v = ? (To be calculated)

And, Focal length, f = + 10 cm (because it is convex lens)

Now, putting these values in the lens formula:

Thus, the position of image is at a distance of 16.67 cm from the lens. The plus sign for image distance shows that the image is formed on the right side of lens (or behind the lens) and that the nature of image is real and inverted.

Let us calculate the magnification now. For a lens:

Magnification,

We will now calculate the size of image h₂ by knowing the size of object h₁ and value of m:

Now,

Thus, the size of image is 3.35 cm. The negative sign of the magnification shows that the image is inverted.

Here, Object distance, u = ? (To be calculated)

Image distance, v =- 10 cm (To the left of concave lens)

Focal length, f =- 15 cm (It is a concave lens)

Now, putting these values in the lens formula:

Putting the values of v and f in the above equation, we get

Object distance, u = -30 cm

Thus, the object is placed at a distance of 30 cm from the concave lens. The minus sign with object distance shows that the object is on its left side. The diagram is shown as:

We can find the position of image by calculating the image distance, v.

Here, Object distance, u =- 10 cm (To the left of mirror)

Image distance, v = ? (To be calculated)

And, Focal length, f = +15 cm (It is a convex mirror)

Putting these values in the mirror formula:

We get:

So, Image distance, v = + 6cm

Thus, the position of image is at a distance of 6 cm from the convex mirror on its right side (behind the mirror). Since the image is formed behind the convex mirror, therefore, the nature of image is virtual and erect.

The plus sign (+) of the magnification shows that the image is virtual and erect. And the value 1 for magnification shows that the image is exactly of the same size as the object. So, the magnification of +1 produced by a plane mirror means that the image formed in a plane mirror is virtual and erect, and of the same size as the object.

Here, Object distance, u = -20 cm (to the left of mirror)

Image distance, v = ? (To be calculated)

Radius of curvature, R = +30cm (It is a convex mirror)

So, Focal length,

Now, putting these values of u and applying formula:

We get:

Thus, the position of image is 8.57 cm behind the mirror (on its right side). Since the image is formed behind the convex mirror, therefore, the nature of image is virtual and erect.

Now,
For a mirror, Magnification, m =

So, m = = + 0.42

So, +0.42 =

h₂ = 0.42×5.0 = 2.1 cm

Thus, the size of image is 2.1 cm.

Here, Object distance, u = -27 cm (To the left side of mirror)

Image distance, v = ? (To be calculated)

Focal length, f = -18 cm (It is a concave mirror)

Height of object, h₁ = 7.0 cm

And, Height of image, h₂ = ? (To be calculated)

Now, For a mirror:

Image distance, v = -54 cm

Since the image distance is minus 54 cm, therefore, the screen should be placed at a distance of 54 cm in front of the concave mirror (on its left side). The nature of image obtained on the screen is real and inverted.

Also, For a mirror,

= -14.0 cm

Thus, the size of image is 14.0 cm.

The power of this lens has a negative sign (or minus sign), indicating its a concave lens. Now,

Power, P = (f= Focal Length)

So, -2.0 =

And,

Or,

So, Focal length of lens, f = -50 cm

The power of this lens is positive (with a plus sign), therefore, this is a convex lens or converging lens. Now,

Power, P =

So, +1.5 =

∴

⇒ f=

So, Focal length of lens, f = +66.7 cm.