An object 2.4 m in front of a lens forms a sharp image on a film 12 cm behind the lens. A glass plate 1 cm thick, of refractive index 1.50 is interposed between lens and film with its plane faces parallel to film. At what distance (from lens) should object shifted to be in sharp focus of film?

Options

A. `7.2 m`
B. `2.4 m`
C. `3.2 m`
D. `5.6 m`

Answer

D

Explanation

Here, `u = - 2.4m = -240 cm, v = 12 cm`.
From `(1)/(f) = (1)/(v) - (1)/(u)`
`= (1)/(12) + (1)/(240) = (20 + 1)/(240) = (7)/(80)cm^(-1)`
As `mu = 1.5`,
real thickness of glass plate, `x = 1 cm`.
`:.` apparent thickness, `y = (x)/(mu) = (1)/(1.5) = (2)/(3)cm`
Shift in image `= x - y = 1 - (2)/(3) = (1)/(3)cm`
`:. v' = 12 - (1)/(3) = (35)/(3)cm u' = ?`
From `(1)/(f) = (1)/(v') - (1)/(f) = (3)/(35) - (7)/(80) = (48 - 49)/(35 xx 16)`
`u' = (-35 xx 16)/(1)cm = - 560 = - 5.6m`
`:.` Object has to be shifted to `5.6 m` from the lens.