The power of a thin convex lens $(\ _{a}n_{g} = 1.5)$ is + 0.5 D. When it is placed in a liquid of refractive index$\ _{a}n_{l,}$ then it behaves as a concave lens of focal length 100 cm. The refractive index of the liquid $\ _{a}n_{l}\ $will be

Question

Dr. Abubacker · Accepted Answer

(a) $5 = (1.5 - 1)\left( \frac{2}{R} \right)\ \ \ \ \ $…(i)
$- 1 = \left( \frac{1.5}{n} - 1 \right)\left( \frac{1}{R} \right)\ \ \ $…(ii)
Dividing Eq.(i) by Eq.(ii), we get
$- 5 = \frac{0.5n}{1.5 - n}$
Or $\  - 7.5 + 5n = 0.5n\ $or$- 7.5 = - 4.5n$
Or $\ n = \frac{75}{45} = \frac{5}{3}$

Q. The power of a thin convex lens $(\ _{a}n_{g} = 1.5)$ is + 0.5 D. When it is placed in a liquid of refractive index$\ _{a}n_{l,}$ then it behaves as a concave lens of focal length 100 cm. The refractive index of the liquid $\ _{a}n_{l}\ $will be

Explanation

Reviewed by Dr. Abubacker

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