Question 322: Ray Optics

Question

Two identical thin plano-convex glass lenses (refractive index 1.5) each having radius of curvature of 20 cm are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index 1.7. The focal length of the combination is

Accepted Answer

We know, $${1 \over f} = (\mu  - 1)\left( {{1 \over {{r_1}}} - {1 \over {{r_2}}}} \right)$$
For the lens on the left,
$${1 \over {{f_1}}} = (1.5 - 1)\left( {{1 \over \infty } - {1 \over { - 20}}} \right) = {1 \over {40}}$$
For the lensh on the right,
$${1 \over {{f_2}}} = (1.5 - 1)\left( {{1 \over { + 20}} - {1 \over \infty }} \right) = {1 \over {40}}$$
For the oil in the intervening space,
$${1 \over {{f_3}}} = (1.7 - 1)\left( {{1 \over { - 20}} - {1 \over {20}}} \right) =  - {7 \over {100}}$$
Hence, if the focal length of the combination is F, then
$${1 \over F} = {1 \over {{f_1}}} + {1 \over {{f_2}}} + {1 \over {{f_3}}} = {1 \over {40}} + {1 \over {40}} - {7 \over {100}} =  - {1 \over {50}}$$
i.e., F = $$-$$50 cm

Answer

$$-$$ 50 cm

Answer

50 cm

Answer

$$-$$ 20 cm

Answer

$$-$$ 25 cm

Ray Optics

Two identical thin plano-convex glass lenses (refractive index 1.5) each having radius of curvature of 20 cm are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index 1.7. The focal length of the combination is

Choose the correct answer: