Question

A convex lens has 20 cm focal length in air. What is its focal length in water? (Refractive index of air-water = 1.33, refractive index of air-glass = 1.5).

Answer 1

SEE THE ANSWER above

Answer 2

Answer:

The focal length in water is 78.125 cm.

Explanation:

Given that,

Focal length in air = 20 cm

Refractive index of air-water n₁= 1.33

Refractive index of air - glass n₂= 1.5

For focal length in air,

Using formula of lens

$\dfrac{1}{f_{air}}=(\dfrac{n_{2}}{n_{1}}-1)\dfrac{1}{R_{1}}-\dfrac{1}{R_{2}}$

Put the value into the formula

$\dfrac{1}{20}=(\dfrac{1.5}{1}-1)(\dfrac{1}{R_{1}}-\dfrac{1}{R_{2}})$

$\dfrac{1}{20}=0.5(\dfrac{1}{R_{1}}-\dfrac{1}{R_{2}})$...(I)

We need to calculate the focal length in water

Using formula of lens

$\dfrac{1}{f_{water}}=(\dfrac{1.5}{1.33}-1)\dfrac{1}{R_{1}}-\dfrac{1}{R_{2}}$

$\dfrac{1}{f_{water}}=0.128\dfrac{1}{R_{1}}-\dfrac{1}{R_{2}}$....(II)

Divided equation (I) by (II)

$\dfrac{f_{water}}{20}=\dfrac{0.5}{0.128}$

$f_{water}=\dfrac{0.5}{0.128}\times20$

$f_{water}=78.125\ cm$

Hence, The focal length in water is 78.125 cm.