A luminous object is separated from a screen by distance d. A convex lens is placed between the object and the screen such that it forms a distinct image on the screen. The maximum possible focal length of this convex lens is

Question

A luminous object is separated from a screen by distance d. A convex lens is placed between the object and the screen such that it forms a distinct image on the screen. The maximum possible focal length of this convex lens is (A) 4d (B) 2d (C) d/2 (D) d/4

Tardigrade Admin · Accepted Answer

Focal length of a convex lens by displacement method
Focal length of the convex lens

f = \frac{a ^{2} - b ^{2}}{4 a}

where

a =

distance between the image and object
and

b =

distance between two positions of lens
Fact The distance between the two points should be greater than four time the focal length of the convex lens, i.e.,

d > 4 f

.
So, the maximum possible focal length of this convex lens is

\frac{d}{4}

.

Q. A luminous object is separated from a screen by distance $d$ . A convex lens is placed between the object and the screen such that it forms a distinct image on the screen. The maximum possible focal length of this convex lens is

$4 d$

$2 d$

$d /2$

$d /4$

Q. A luminous object is separated from a screen by distance d. A convex lens is placed between the object and the screen such that it forms a distinct image on the screen. The maximum possible focal length of this convex lens is

4d

2d

d/2

d/4

Q. A luminous object is separated from a screen by distance $d$ . A convex lens is placed between the object and the screen such that it forms a distinct image on the screen. The maximum possible focal length of this convex lens is

$4 d$

$2 d$

$d /2$

$d /4$