Question 367: Ray Optics

Question

Two identical glass ($$\mu $$g = 3/2) equiconvex lenses of focal length $$f$$ each are kept in contact. The space between the two lenses is filled with water $$\left( {{\mu _w} = 4/3} \right)$$. The focal length of the combination is

Accepted Answer

Focal length (f) of glass convex lens is given by
$${1 \over f} = \left( {{\mu _g} - 1} ight)\left( {{2 \over R}} ight)$$
$$ \Rightarrow $$ $${1 \over f} = \left( {{3 \over 2} - 1} ight)\left( {{2 \over R}} ight)$$
$$ \Rightarrow $$ f = R
Focal length (f
1
) of water filled concave lens is given by
$${1 \over {{f_1}}} = \left( {{\mu _w} - 1} ight)\left( { - {2 \over R}} ight)$$
$$ \Rightarrow $$ $${1 \over {{f_1}}} = \left( {{4 \over 3} - 1} ight)\left( { - {2 \over R}} ight)$$ = $${ - {2 \over {3R}}}$$ = $${ - {2 \over {3f}}}$$
Equivalent focal length (f
eq
) of lens system
$${1 \over {{f_{eq}}}} = {1 \over f} - {2 \over {3f}} + {1 \over f}$$ = $${4 \over {3f}}$$
$$ 	herefore $$ f
eq
= $${{3f} \over 4}$$

Answer

$$f/3$$

Answer

$$f$$

Answer

$$4f/3$$

Answer

$$3f/4$$

Ray Optics

Two identical glass ($\mu g = 3/2) equiconvex lenses of focal length f each are kept in contact. The space between the two lenses is filled with water \left( {{\mu _w} = 4/3} \right)$. The focal length of the combination is

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