An object 2 . 4 m in front of a lens forms a sharp image on a screen 12 cm behind the lens. A glass plate 1 cm thick, of refractive index 1 . 50 is interposed between lens and screen with its plane faces parallel to screen. At what distance from the lens, should object be placed so as to get a sharp image on the screen?

Step-by-step solution

According to the thin lens formula 1 f ⁡ = 1 v ⁡ - 1 u ⁡ Here, u = - 2 . 4 m = - 240 cm , v = 12 cm ∴ 1 f ⁡ = 1 1 2 - 1 - 2 4 0 = 1 1 2 + 1 2 4 0 1 f ⁡ = 2 1 2 4 0 or f ⁡ = 2 4 0 2 1 cm When a glass plate is interposed between lens and film, so shift produced by it will be Shift = t 1 - 1 μ = 1 1 - 1 1 . 5 = 1 1 - 2 3 = 1 3 cm To get an image at the film, the lens should form an image at a distance v ⁡ ' = 1 2 - 1 3 = 3 5 3 cm Again using lens formula ∴ 2 1 2 4 0 = 3 3 5 - 1 u ⁡ ′ or 1 u ⁡ ′ = 3 3 5 - 2 1 2 4 0 = 1