Question

A thin plano-convex lens of focal length 73.5 cm has a circular aperture of diameter 8.4 cm. If the refractive index of the material of the lens is \( \frac{5}{3} \), then the thickness of the lens is nearly.

• A. \(2.4 \, \text{cm}\)
• B. \(2.4 \, \text{mm}\)
• C. \(1.8 \, \text{cm}\)
• D. \(1.8 \, \text{mm}\) \bigskip

Hint:

Use the formula for thickness in plano-convex lenses to determine the size of the lens using the refractive index and radius of curvature.

Answer 1

The Correct Option is C

Step 1: For a plano-convex lens, the approximate thickness of the lens \( t \) can be calculated using the formula: \[ t = \frac{R}{n - 1} \] where \( R \) is the radius of curvature, and \( n \) is the refractive index. Here, \( R = \frac{D}{2} = \frac{8.4}{2} = 4.2 \, \text{cm} \), and \( n = \frac{5}{3} \). Now, substituting the values: \[ t = \frac{4.2}{\frac{5}{3} - 1} = \frac{4.2}{\frac{2}{3}} = 4.2 \times \frac{3}{2} = 1.823 \, \text{cm} \] The thickness of the lens is approximately \( \boxed{1.8 \, \text{cm}} \).