Question

Two plane mirrors are at an angle such that a ray incident on a mirror may undergo a total deviation of 240° after two reflections.

• A. The angle between the mirror is 60°.
• B. The number of images formed by this system is 5, if an object is placed symmetrically between the mirror.
• C. The number of image is 5, if an object is kept unsymmetrical between the mirror.
• D. None of these

Answer 1

Answer: (A), (B), (C)

A, B, C

Answer 2

The problem involves two main concepts: the total deviation of a light ray after two reflections from inclined mirrors, and the number of images formed by such a system.

1. Angle between the mirrors ($\theta$):

When a light ray undergoes two reflections from two plane mirrors inclined at an angle $\theta$, the total deviation ($\delta$) of the ray is given by the formula:

$$\delta = 360^\circ - 2\theta$$

Given that the total deviation $\delta = 240^\circ$.

Substituting this value into the formula:

$$240^\circ = 360^\circ - 2\theta$$

Rearranging the equation to solve for $2\theta$:

$$2\theta = 360^\circ - 240^\circ$$ $$2\theta = 120^\circ$$

Dividing by 2:

$$\theta = 60^\circ$$

Therefore, the angle between the mirrors is 60°. This confirms Option A is correct.

2. Number of images formed (N):

The number of images formed by two plane mirrors inclined at an angle $\theta$ is determined by the value of $\frac{360^\circ}{\theta}$.

In this case, $\theta = 60^\circ$. Let's calculate $\frac{360^\circ}{\theta}$:

$$\frac{360^\circ}{60^\circ} = 6$$

Since $\frac{360^\circ}{\theta}$ is an even integer (6 is an even integer), the number of images formed is given by the formula:

$$N = \frac{360^\circ}{\theta} - 1$$

Substituting the value:

$$N = 6 - 1$$ $$N = 5$$

When $\frac{360^\circ}{\theta}$ is an even integer, the number of images formed is always $\left(\frac{360^\circ}{\theta} - 1\right)$, regardless of whether the object is placed symmetrically or unsymmetrically between the mirrors.

Therefore:

• If an object is placed symmetrically between the mirrors, the number of images is 5. This confirms Option B is correct.
• If an object is kept unsymmetrically between the mirrors, the number of images is also 5. This confirms Option C is correct.

Since options A, B, and C are all correct, option D ("None of these") is incorrect.