Two plane mirrors at an angle such that a ray incident on a mirror undergoes a total deviation of `240^(@)` after two reflections:

Options

A. the angle between the mirrors is `60^(@)`
B. the number of images formed by this system will be `5` , if an object is placed symmetrically between the mirrors
C. the number of images will be 5 if an object is kept unsymmetrical between the mirrors
D. a ray will retrace its path after 2 successive reflections , if the angle of incidence on one mirror is `60^(@)`

Answer

A,B,C,D

Explanation

If the angle between mirrors be `theta` then the angle of deviation after two reflections is `delta = 2pi-20`
`240 = 2 xx 180^(@)- 2 theta`
`2theta = 360 - 240`
`2theta = 120 (theta=60^(@))`
Hence[A]

`therefore m = (360^(@))/(60) = 6 ( even)

Number of images = n= m-1 = 6-1 = 5
[Hence (B) & (C).
Reflected ray from `M_(1)`' strikes `bot`' on mirror `'M_(2)`'
Hence retrace its path. Hence [D].