Back to Directory
NEET PHYSICSMedium

The power of a biconvex lens is 10 dioptre and the radius of curvature of each surface is 10 cm. The refractive index of the material of the lens is:

A

4/3

B

9/8

C

5/3

D

3/2

Step-by-Step Solution

  1. Identify Given Data:
  • Power of the lens, P=+10 DP = +10 \text{ D} (converging lens).
  • Radius of curvature, R=10 cm=0.1 mR = 10 \text{ cm} = 0.1 \text{ m}.
  • For a biconvex lens, using the sign convention: R1=+RR_1 = +R and R2=−RR_2 = -R.
  1. Lens Maker's Formula: The power of a lens is given by: P=(μ−1)(1R1−1R2)P = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)
  2. Calculation: Substituting the values into the formula: 10=(μ−1)(10.1−1−0.1)10 = (\mu - 1) \left( \frac{1}{0.1} - \frac{1}{-0.1} \right) 10=(μ−1)(10.1+10.1)10 = (\mu - 1) \left( \frac{1}{0.1} + \frac{1}{0.1} \right) 10=(μ−1)(20.1)10 = (\mu - 1) \left( \frac{2}{0.1} \right) 10=(μ−1)(20)10 = (\mu - 1) (20) μ−1=1020=0.5\mu - 1 = \frac{10}{20} = 0.5 μ=1+0.5=1.5=32\mu = 1 + 0.5 = 1.5 = \frac{3}{2}
  3. Conclusion: The refractive index of the material is 1.5 or 3/2.
Practice Mode Available

Master this Topic on Sushrut

Join thousands of students and practice with AI-generated mock tests.

Get Started