The graph shows how the magnification m produced by a thin lens varies with image distance v. What is the focal length of the lens used ?

Question

The graph shows how the magnification m produced by a thin lens varies with image distance v. What is the focal length of the lens used ? (A) (b2 c/a) (B) (b2/ac) (C) (a/c) (D) (b/c)

Tardigrade Admin · Accepted Answer

(1/v) - (1/u) = (1/f) 1- (v/u) = (v/f) 1-m = (v/f) m = 1 - (v/f) At v =a , m1 =1 - (a/f) At v = a +b, m2 = 1 - (a+b/f) m2 -m1 =c = [1- (a+b/f)] - [1- (a/f)] c = (b/f) f= (b/c)

Q. The graph shows how the magnification $m$ produced by a thin lens varies with image distance $v$ . What is the focal length of the lens used ?

$\frac{b ^{2} c}{a}$

$\frac{b ^{2}}{a c}$

$\frac{a}{c}$

$\frac{b}{c}$

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$
$1 - \frac{v}{u} = \frac{v}{f}$
$1 - m = \frac{v}{f}$
$m = 1 - \frac{v}{f}$
At $v = a, m_{1} = 1 - \frac{a}{f}$
At $v = a + b, m_{2} = 1 - \frac{a + b}{f}$
$m_{2} - m_{1} = c = [1 - \frac{a + b}{f}] - [1 - \frac{a}{f}]$
$c = \frac{b}{f}$
$f = \frac{b}{c}$

Q. The graph shows how the magnification m produced by a thin lens varies with image distance v. What is the focal length of the lens used ?

ab2c​

acb2​

ca​

cb​