Two identical glass equiconvex lenses of focal length each are kept in contact. The space between the two lenses is filled with water . The focal length of the combination is [2016]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
Two identical glass $(μ_{g} = 3 / 2)$ equiconvex lenses of focal length $f$ each are kept in contact. The space between the two lenses is filled with water $(μ_{w} = 4 / 3)$ . The focal length of the combination is [2016]

1 $f / 3$

2 $f$

3 $4 f / 3$

4 $3 f / 4$

Ans.
(4)

Here, $μ_{g} = \frac{3}{2}, μ_{w} = \frac{4}{3}$

Focal length $(f)$ of glass convex lens is given by

$\frac{1}{f} = (μ_{g} - 1) (\frac{2}{R})$

or $\frac{1}{f} = (\frac{3}{2} - 1) \frac{2}{R} = \frac{1}{R} or f = R$ ...(i)

Focal length $(f')$ of water filled concave lens is given by

$\frac{1}{f'} = (μ_{w} - 1) (- \frac{2}{R}) or \frac{1}{f'} = (\frac{4}{3} - 1) (- \frac{2}{R})$

$= - \frac{2}{3 R} = - \frac{2}{3 f} [Using eqn. (i)]$

Equivalent focal length $(f_{eq})$ of lens system

$\frac{1}{f_{eq}} = \frac{1}{f} - \frac{2}{3 f} + \frac{1}{f} = \frac{3 - 2 + 3}{3 f} = \frac{4}{3 f} ∴ f_{eq} = \frac{3 f}{4}$

Want Us to Email you About Special Offers & Updates?