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Physics Question 47 – JEE-MAIN 2026

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Some distant star is to be observed by some telescope of diameter of objective lens a, at an angular resolution of 3.0×10−7 radian. If the wavelength of light from the star reaching the telescope is 500 nm, the minimum diameter of the objective lens of the telescope is _______ cm. (nearest integer)

The ability of a telescope to distinguish between two closely spaced objects is limited by the diffraction of light, which is described by Rayleigh's criterion.

Step 1: Identify the relevant formula for angular resolution✦ Active

The angular resolution θ of a telescope with a circular objective lens of diameter D for light of wavelength λ is given by Rayleigh's criterion:

θ=1.22λD
Step 2: Convert given values to consistent units and rearrange the formula○ Expand

Given angular resolution θ=3.0×10−7 rad and wavelength λ=500 nm=500×10−9 m=5×10−7 m. Rearranging the formula to solve for the diameter D:

D=1.22λθ
💡 Teacher's Secret Hint

Ensure all units are in SI base units (meters, radians) before calculation to avoid errors.

Step 3: Substitute values, calculate diameter, and convert to the required unit○ Expand

Substitute the given values into the rearranged formula:

D=1.22×5×10−7 m3.0×10−7 rad=1.22×53 m

Calculate the value:

D≈1.22×1.6667 m≈2.0333 m

Convert the diameter from meters to centimeters and round to the nearest integer:

D=2.0333×100 cm=203.33 cm

Rounding to the nearest integer, the minimum diameter of the objective lens is 203 cm.

💡 Teacher's Secret Hint

Pay attention to the final unit requested (cm) and the rounding instruction (nearest integer).

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