Mirrors Placed At An Angle

Concept Explanation

Mirrors Placed At An Angle

Multiple Reflection

We know that plane mirror reflects light falling on it. This reflected ray can act as incident ray for another mirror. This process of reflection of light several times between reflecting surfaces is known as Multiple reflection of light.

Multiple reflection can be obtained by placing more than one mirror at certain angle to each other which results in reflection of light for multiple times between reflecting surfaces.

Mirrors Placed At An Angle: In case of multiple reflections the ray that is incident on one mirror after getting reflected at more that one mirror bounces back in the same medium. Applying the laws of reflection we can calculate the angle at which it will bounce back.

Illustration: Two mirrors are inclined at an angle of 120⁰ . A ray is incident on mirror M1 at an angle of 65⁰to the normal. Find the direction of the ray after it is reflected from mirror M2.

Solution: The diagram showing the arrangement of the mirrors is as follows:

At mirror M₁ the incident ray makes an angle of 65⁰ with the normal. So,

Angle of incidence i = 65⁰

According to the laws of reflection angle of reflection r = 65⁰

As the normal makes an angle of 90⁰ with the surface of the mirror

So the reflected ray makes an angle of = 90⁰ - 65⁰ = 25⁰ with the surface of the mirror M₁

The reflected ray forms a triangle AOB with the two mirror surfaces,

Now $angle BAO = 25^0$

$angle AOB = 120^0$

From angle sum property of triangle AOB

$angle AOB + angle BAO + angle ABO = 180^0$

$Rightarrow ;;120^0 + 25^0 + angle ABO = 180^0$

$Rightarrow ;;145^0 + angle ABO = 180^0$

$Rightarrow ;; angle ABO = 180^0 - 145^0= 35^0$

The first reflected ray is incident on mirror M₂and makes an angle of 35⁰with the surface of the mirror

The incident ray makes angle of = 90⁰ - 35⁰ = 55⁰ with the normal to the surface of the mirror M₂

Now angle of incidence for mirror M₂ = 55⁰

According to the laws of reflection angle of reflection r = 55⁰

Hence the second reflected ray makes an angle of 55⁰ with the normal to the surface of the mirror M₂

Number of Images Formed By An Inclined Mirrors:

The number of images formed by two plane mirrors depends on the angle between them. If two plane mirrors are placed at an angle of X degree, then the number of images formed (n) is given by the formula

Formula to find number of images formed when two mirrors are placed side by side

$Number ;of ;images = frac{360}{X}-1,;;;;;if; frac{360}{X}; is; even$

$Number ;of ;images = frac{360}{X},;;;;;if; frac{360}{X}; is; odd$

Illustration: Find the number of images formed when angle between two mirrors is $180^{circ}$ .

Solution: By using formula we get

$frac{360}{180}-1Rightarrow 2-1=1$

which means only one image is formed .

Illustration: Find the number of images formed when angle between two mirrors is $90^{circ}$ .

Solution: By using formula we get

$frac{360}{90}-1Rightarrow 4-1=3$

which means 3 images will be formed .

Sample Questions

(More Questions for each concept available in Login)

Question : 1

Which of the following are correct ? (a) This process of reflection of light several times between more than one reflecting surfaces is known as multiple reflection of light. (b) In case of multiple reflections the ray that is incident on one mirror after getting reflected at more that one mirror bounces back in the same medium .
A. Only (a) is correct .	B. Only (b) is correct .	C. Both (a) and (b) is correct .	D. None of these .
Right Option : C
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Question : 2

In case of ____________________ the ray that is incident on one mirror after getting reflected at more that one mirror bounces back in the same medium.
A. Multiple reflection	B. Multiple refraction	C. Multiple dispersion	D. None of these .
Right Option : A
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Question : 3

This process of reflection of light several times between more than one reflecting surfaces is known as ___________________ .
A. Law reflection of light	B. Regular reflection of light	C. Multiple reflection of light	D. None of these .
Right Option : C
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