A Plano-convex lens is made of a material of refractive index n. When a small object is placed 30cm away in front of the curved surface of the lens, an image of double the size of the object is produced. Due to reflection from the convex surface of the lens , another faint image is observed at a distance of 10 cm away from the lens, Which of the following statement (s) is(are)true?

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The refractive index of the lens is 2.5

The radius of curvature of the convex surface is 45cm

The faint image is erect and real

The focal length of the lens is 20cm

answer is A, D.

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Detailed Solution

Reflecting curved surface behaves as a convex mirror
$\begin{array}{l} \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \\ \Rightarrow \frac{1}{+ 10} + \frac{1}{- 30} = \frac{1}{f} \\ \Rightarrow f = + 15 c m \\ \Rightarrow R = 2 f = 30 c m \end{array}$

For lens:
$m = \frac{f}{f + u}$
For real image ‘m’ is negative
$\begin{array}{l} - 2 = \frac{f}{f - 30} \\ \Rightarrow f - 30 = - \frac{f}{2} \\ \Rightarrow \frac{3 f}{2} = 30 \\ \Rightarrow f = 20 c m \\ L e n s M a k e r s F o r m u l a : f = \frac{R}{μ - 1} = 20 \\ \Rightarrow \frac{30}{μ - 1} = 20 \\ \Rightarrow μ = 2.5 \end{array}$