Ray Optics

JEE Main level, single correct, medium

125 of 295

Question 125 of 295

A convex lens is made from glass material having refractive index of 1.41.4 with same radius of curvature on both sides. The ratio of its focal length and radius of curvature is ______.

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Answer: (D) 1.251.25

Using the lens maker's formula:

1f=(μ−1)(1R1−1R2)\dfrac{1}{f} = (\mu - 1) \left( \dfrac{1}{R_1} - \dfrac{1}{R_2} \right)

For an equiconvex lens, R1=RR_1 = R and R2=−RR_2 = -R. Given μ=1.4\mu = 1.4:

1f=(1.4−1)(1R−1−R)\dfrac{1}{f} = (1.4 - 1) \left( \dfrac{1}{R} - \dfrac{1}{-R} \right)

1f=0.4×2R\dfrac{1}{f} = 0.4 \times \dfrac{2}{R}

1f=0.8R\dfrac{1}{f} = \dfrac{0.8}{R}

fR=10.8=1.25\dfrac{f}{R} = \dfrac{1}{0.8} = 1.25

Answer: 1.251.25

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