2 plane mirror are inclined at angle 120. The distance between the two images formed by plane mirror is 20 cm . If the object is placed symmetrically between those 2 mirrors. Then find the distance of object from intersection of mirrors ?

Question

Answer

11.5

Answer

Solution:

Given:
- Two plane mirrors are inclined at an angle of 120 degrees.
- The distance between the two images formed by plane mirror is 20 cm.
- The object is placed symmetrically between the two mirrors.

To find:
- The distance of the object from the intersection of mirrors.

Explanation:

When an object is placed between two plane mirrors inclined at an angle, multiple images are formed. The number of images formed is given by the formula:

n = 360/θ - 1

where n is the number of images formed and θ is the angle between the mirrors.

In this case, the angle between the mirrors is 120 degrees, so the number of images formed is:

n = 360/120 - 1 = 2

Therefore, two images are formed.

Let the distance of the object from the intersection of the mirrors be x. The distance between each image and the intersection of the mirrors is also x.

Using the formula for the distance between two images formed by two plane mirrors inclined at an angle θ:

d = Dsin(θ/2)

where d is the distance between the two images, D is the distance of the object from the mirrors, and θ is the angle between the mirrors.

In this case, θ = 120 degrees and d = 20 cm. Substituting these values, we get:

20 = 2xsin(120/2)

20 = 2xsin(60)

20 = 2x(√3/2)

x = 5√3 cm

Therefore, the distance of the object from the intersection of the mirrors is 5√3 cm.

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