Wave Optics

JEE Main level, single correct, medium

123 of 191

Question 123 of 191

A telescope with objective diameter RR is used to observe a distant star emitting light of wavelength 500500 nm, at a resolution of 5×10−75 \times 10^{-7} radian. The value of RR is _____ cm.

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Answer: (B) 122122

The limit of resolution of a telescope is given by the formula:

Δθ=1.22λR\Delta \theta = \dfrac{1.22 \lambda}{R}

where λ\lambda is the wavelength of light and RR is the diameter of the objective lens.

Given:
λ=500 nm=500×10−9 m=5×10−7 m\lambda = 500 \text{ nm} = 500 \times 10^{-9} \text{ m} = 5 \times 10^{-7} \text{ m}
Δθ=5×10−7 rad\Delta \theta = 5 \times 10^{-7} \text{ rad}

Substituting the values into the formula:

5×10−7=1.22×5×10−7R5 \times 10^{-7} = \dfrac{1.22 \times 5 \times 10^{-7}}{R}

R=1.22 mR = 1.22 \text{ m}

Converting to centimeters:

R=1.22×100 cm=122 cmR = 1.22 \times 100 \text{ cm} = 122 \text{ cm}

Answer: 122122

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