A glass slab of thickness 2cm and refractive index 2 is placed in contact with a biconvex lens of focal length 20cm. The refractive index of the material of the lens 1.5 . The far side of the lens is silvered. Where should an object be placed in front of the slab so that it images on to itself?

Explanation

To solve the problem, we need to determine where to place an object in front of a glass slab and biconvex lens system so that the image formed is at the same location as the object. Here’s a step-by-step solution:

### Step 1: Understand the System
We have a glass slab of thickness \( t = 2 \, \text{cm} \) and refractive index \( \mu = 2 \) placed in contact with a biconvex lens with a focal length \( f = 20 \, \text{cm} \) and refractive index \( \mu_l = 1.5 \). The far side of the lens is silvered, making it act like a concave mirror.

### Step 2: Calculate the Apparent Shift due to the Glass Slab
The apparent shift \( d \) caused by the glass slab can be calculated using the formula:
\[
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