A ray of light is incident on the surface of a glass plate of thickness `t`. If the angle of incidence `theta` is small, the emerging ray would be displaced side ways by an amount
(Take `n` = refractive index of glass)

Options

A. `t(1-(i)/(r))`
B. `t(1-(i)/(r))`
C. `it(1-(r)/(i))`
D. `t(1-(r)/(i))`

Answer

C

Explanation

From figure, in right angle `DeltaCDB`
`/_CBD=(i-r)`
`:.sin(i-r)=(CD)/(BC)=(d)/(BC)`
or `d=BCsin(i-r)` ...(i)
Also, in right angled `DeltaCNB`
`cosr=(BN)/(BC)=(t)/(BC)` or
`BC=(t)/(cosr)` ...(ii)
Now, from equation (i), we get `d=(t)/(cosr)sin(i-r)`
For small angles `sin(i-r)~~i-r, cosr~~1`
`d=t(i-r), d=it(1-(r)/(i))`