JEE Main 2026 — Apr 4, Shift 1 — Physics solution

JEE Main2026Apr 4, Shift 1Physics

A telescope with objective diameter $R$ is used to observe a distant star emitting light of wavelength $500$ nm, at a resolution of $5 \times 1 0^{- 7}$ radian. The value of $R$ is _______ cm.

A
$61$
B
$122$
C
$244$
D
$305$

Solution

Rayleigh criterion for a circular aperture: $θ_{m i n} = \frac{1.22 λ}{R} .$

$R = \frac{1.22 \times 500 \times 1 0 ^{- 9}}{5 \times 1 0 ^{- 7}} = \frac{6.1 \times 1 0 ^{- 7}}{5 \times 1 0 ^{- 7}} = 1.22 m = 122 cm .$

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