Question

A ray parallel to the x-axis (principal axis of curved surface) is incident. The x-coordinate where the ray cuts the x-axis is: (The radius of curvature is 50 cm and \( \mu = 1.5 \)).

• A. 1.5
• B. 0.5
• C. 1
• D. 2

Hint:

In optics problems involving curved surfaces, use the lens maker's formula to find the position of rays after refraction.

Answer 1

The Correct Option is A

Step 1: Use the lens maker's formula.
The ray undergoes refraction as it passes through a curved surface. The formula for the x-coordinate where the ray cuts the axis can be derived from the lens maker's equation: \[ x = \frac{R}{\mu - 1} \] where \( R \) is the radius of curvature and \( \mu \) is the refractive index. Step 2: Apply the given values.
Given that the radius of curvature \( R = 50 \, \text{cm} \) and \( \mu = 1.5 \), we substitute these values into the formula: \[ x = \frac{50}{1.5 - 1} = \frac{50}{0.5} = 1.5 \] Step 3: Conclusion.
Thus, the x-coordinate where the ray cuts the x-axis is 1.5 m. Final Answer: \[ \boxed{1.5} \]