Question 326: Ray Optics

Question

A compound microscope consists of an
objective lens of focal length 1 cm and an
eyepiece of focal length 5 cm with a separation
of 10 cm.
The distance between an object and the
objective lens, at which the strain on the eye is
minimum is $${n \over {40}}$$ cm. The value of n is _____.

Accepted Answer

Given, L = |v
0
| + |u
e
| = 10 cm
(v
e
= $$\infty $$)
$${1 \over {{v_e}}} - {1 \over {{u_e}}} = {1 \over {{f_e}}}$$
$$ \Rightarrow $$ $${1 \over \infty } - {1 \over {{u_e}}} = {1 \over 5}$$
$$ \Rightarrow $$ u
e
= -5
$$ \Rightarrow $$ |u
e
| = 5 cm
$$ 	herefore $$ |v
0
| + 5 = 10 cm
$$ \Rightarrow $$ |v
0
| = 5 cm
For objective, v
0
= 5 cm, f
0
= 1 cm
$${1 \over {{v_0}}} - {1 \over {{u_0}}} = {1 \over {{f_0}}}$$
$$ \Rightarrow $$ $${1 \over 5} - {1 \over {{u_0}}} = {1 \over 1}$$
$$ \Rightarrow $$ u
0
= $$ - {5 \over 4}$$
$$ \Rightarrow $$ |u
0
| = $${5 \over 4}$$ = $${{50} \over {40}}$$ = $${n \over {40}}$$
$$ 	herefore $$ n = 50

Ray Optics

A compound microscope consists of an objective lens of focal length 1 cm and an eyepiece of focal length 5 cm with a separation of 10 cm. The distance between an object and the objective lens, at which the strain on the eye is minimum is ${n \over {40}}$ cm. The value of n is _____.

Choose the correct answer: