JEE MAIN - Physics (2021 - 17th March Morning Shift - No. 11)
The thickness at the centre of a plane convex lens is 3 mm and the diameter is 6 cm. If the speed of light in the material of the lens is 2 $$\times$$ 108 ms$$-$$1. The focal length of the lens is ____________.
0.30 cm
30 cm
15 cm
1.5 cm
Explanation
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$${R^2} = {3^2} + {(R - 0.3)^2}$$
$$ \Rightarrow $$ $${R^2} = 9 + {R^2} + 0.09 - 2 \times 0.3R$$
$$ \Rightarrow $$ $$2 \times 0.3R = 9.09$$
$$ \Rightarrow $$ $$R = 15.15$$ cm
$$\mu = {C \over V}$$ = $${{3 \times {{10}^8}} \over {2 \times {{10}^8}}}$$ = 1.5
$${1 \over f} = (1.5 - 1)\left( {{1 \over R}} \right)$$
$$f \simeq 30$$ cm
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