JEE Main 2026 · 4 April · morning · Single correct · +4 / −1
A telescope with objective diameter R is used to observe a distant star emitting light of wavelength 500 nm , at a resolution of 5× 10⁻⁷ radian. The value of R is
____ cm .
- (a) 61
- (b) 122
- (c) 244
- (d) 305
Answer and solution
Answer (b) 122
Solution
Physics sir · 3 steps
Use the Rayleigh limit θ = 1.22λ/D and solve for the diameter.
- Rayleigh criterion. Light from a star passes through the circular objective and spreads into a diffraction pattern. The smallest angle the telescope can resolve depends on the wavelength and the objective's diameter D.
θ = (1.22 λ)/D ⇒ D = (1.22 λ)/θ
- Put in numbers. With λ = 500 nm = 5 × 10⁻⁷ m and θ = 5 × 10⁻⁷ rad, we get D = (1.22 × 5 × 10⁻⁷)/(5 × 10⁻⁷) = 1.22 m.
- So. R = 1.22 m = 122 cm, which is option (b).
The idea to keep. For any circular aperture, the limit of resolution is 1.22λ/D, with D the full diameter. A bigger objective or a shorter wavelength resolves finer detail.
Answer from the NTA final answer key. Solution by PrepWiser.