Physics Q44 – JEE-MAIN 2026

A telescope with objective diameter

D

is used to observe a distant star emitting light of wavelength

500 nm

, at a resolution of

5 \times 10^{- 7}

radian. The value of

D

is _______ cm.

Clue 1 of 3: Understanding Resolution

The resolution of a telescope refers to its ability to distinguish between two closely spaced objects.

🧠 Full Solution Path

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

The angular resolution $θ$ of a telescope is given by the Rayleigh criterion:

θ = \frac{1.22 λ}{D}

where $λ$ is the wavelength of light and $D$ is the diameter of the objective.

Step 2: Substitute the given values and solve for D○ Expand

Given wavelength $λ = 500 nm = 500 \times 10^{- 9} m = 5 \times 10^{- 7} m$ and resolution $θ = 5 \times 10^{- 7} radian$ . Rearranging the formula to solve for $D$ :

D = \frac{1.22 λ}{θ}

Substituting the values:

D = \frac{1.22 \times (5 \times 10^{- 7} m)}{5 \times 10^{- 7} radian} = 1.22 m

💡 Teacher's Secret Hint

Ensure consistent units (meters for length) before performing the calculation.

Step 3: Convert the diameter to the required unit (cm)○ Expand

The question asks for the value of $D$ in cm. Convert the calculated diameter from meters to centimeters:

D = 1.22 m = 1.22 \times 100 cm = 122 cm

💡 Teacher's Secret Hint

Always double-check the final unit requested in the question.

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Physics Question 44 – JEE-MAIN 2026

Clue 1 of 3: Understanding Resolution

🧠 Full Solution Path