Question

A)The magnifying power of a simple microscope is 6. The focal length of its lens in meters will be ? (Least distance of distinct visionis 25cm)
A. 0.05
B.0.06
C.0.25
D.0.12

B) the focal length of one lens is -40 cm and that if the other is +20 cm . The foxal length of this combination wil be
A.15.2cm
B.40cm
C.-40cm
D.35cm

Answer 1

Answer:

A) Option A 0.05

B) Option B 40 cm

Explanation:

(A) Magnification of the lens

$M=6$

Least distance of Distinct vision

$D=25$ cm

We know that if focal length of the lens is f then

$\boxed{M=1+\frac{D}{f}}$

$\implies 6=1+\frac{25}{f}$

$\implies \frac{25}{f}=5$

$\implies f=\frac{25}{5}$ cm

$\implies f=5$ cm

or, $f=0.05$ m

(B) Given two focal lengths

$f_1=-40$ cm

$f_2=+20$ cm

Power of the lens is reciprocal of the focal length

Power of the lenses will be

$P_1=\frac{1}{f_1}=\frac{1}{-40}=-\frac{1}{40}$

$P_2=\frac{1}{f_2}=\frac{1}{20}$

Combined power of the lens

$P=P_1+P_2$

$\implies P=-\frac{1}{40}+\frac{1}{20}$

$\implies P=\frac{-1+2}{40}$

$\implies P=\frac{1}{40}$

Therefore, the combined focal length will be

$F=\frac{1}{P}$

$\implies F=\frac{1}{1/40}$

$\implies F=40$ cm

Hope this helps.