A thin biconvex lens of refractive index 3/2 is placed on a horizontal plane mirror as shown in Fig.
The space between the lens and the mirror is filled with a liquid of refractive index 4/3. It is found that when a point object is placed 15 cm above the lens on its principal axis, the object coincides with its own image. On repeating with another liquid, the object and the image again coincide at a distance 25 cm from the lens. Calculate the refractive index of the liquid.
Text Solution
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Sol. The light retraces its path if it is incident normally on a mirror. The rays after refraction through the lens and the liquid are parallel. We will apply the general thin lens equation with parameters,
n 1 = 1, n 2 = 3/2, n 3 = 4/3, u = 15 cm. and v = ∞
– 
= 
+ 
– 
= 
– 
On solving for R we get R = 10 cm. Similarly, when second liquid is filled, we have
– 
= 
– 
On solving for 
we get, 
= 1.6
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