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Question

A mark is made on the bottom of a vessel, over this mark a glass slab of thickness 3.5cm and refractive index 74 is placed. Now water (refractive index 43) is poured into the vessel so that the surface of the water is 8 cm above the upper surface of the slab. Looking down normally through the water, the apparent depth of the mark below the surface of the water will be


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Solution

Step 1. Given data:

The thickness of the glass slab tg = 3.5cm

Refractive index of glass slab μg = 74

Refractive index of water μw = 43

Step 2. Formula used:

Refractive index μ = drealdapparent,

Where dreal=real depth, dapparent=apparent depth

Step 3. Calculating apparent depth.

Hence dapparent=drwμw+drgμg,

Where drw=real depth of water, drg=real depth of glass

Thus, apparent depth = 843+3.574=8cm

Thus, the apparent depth of the mark below the surface will be 8cm.


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