Question

A microscope has an objective of 10mm focal length and eye piece has of 25mm focal length. What is the distance between the lenses if the object is in sharp focus shen it is 10.5mm from the object

Answer 1

HELLO DEAR,

GIVEN:-
$\bold{f_o}$ = focal length if objective length = 10mm
$\bold{f_e}$ = focal length of eye lense = 25mm
$\bold{v_o}$ = distance between image and objective lense
$\bold{u_o}$ = distance between object and objective lens = -10.5mm

according to lens formula we know that

$\bold{\qquad \frac{1}{f_o} = \frac{1}{v_o} - \frac{1}{u_o}}$

$\bold{\qquad \frac{1}{10} = \frac{1}{v_o} - \frac{1}{-10.5}}$

$\bold{\qquad \frac{1}{v_o} = \frac{1}{10} - \frac{1}{10.5}}$

$\bold{\qquad \frac{1}{v_o} = \frac{10.5 - 10}{105}}$

$\bold{\qquad \frac{1}{v_o} = \frac{0.5}{105}}$

$\bold{\qquad \frac{1}{v_o} = 5/1050}$

$\bold{\qquad v_o = 210mm}$

the formula for distance beetwen two lenses is $\bold{L = v_o + f_e}$ = 210mm + 25mm

$\bold{L = 235mm = 23.5cm}$

I HOPE IT'S HELP YOU DEAR,
THANKS

Answer 2

Hii friend,

Given-

Focal length of objective fo = 10mm = 1cm

Focal length of eyepiece fe = 25mm = 2.5cm

Object distance for objective uo = -10.5mm = 1.05cm

Image distance vo = ?

Image distance for eyepiece ve = -25cm

Object distance ue = ?

To find-

Distance between two lenses d = ?

Solution-

Lens formula states

1/fo = 1/vo - 1/uo

1/vo = 1/fo + 1/uo

1/vo = 1/1 + 1/-1.05

1/vo = (1.05-1)/1.05×1

1/vo = 0.05/1.05

vo = 105/5 = 21cm

Lens formula states

1/f e = 1/ve - 1/ue

1/ue = 1/v e - 1/fe

1/ue = 1/-25 - 1/2.5

1/ue = (-1-10)/25

1/ue = -11/25

ue = -25/11

ue = -2.27cm

But

distance between 2 lenses given by

d = |ue| + vo

d = 2.27 + 21

d = 23.27 cm