Explanation
1. Given Data
2. Concept and Formula
According to Rayleigh's Criterion for a circular aperture (like a telescope's objective lens), two point sources are just resolvable when the central maximum of the diffraction pattern of one source falls on the first minimum of the diffraction pattern of the other.
The formula for the minimum angular separation (θmin) in radians is given by:
θmin=D1.22λ
Where:
θmin is the limit of resolution (angular separation in radians).
λ is the wavelength of the light used.
D is the aperture diameter of the objective lens.
3. Step-by-Step Calculation
Substitute the converted standard values into the formula:
θmin=5×10−2 m1.22×(5×10−7 m)
Cancel out the common value 5 from the numerator and denominator:
θmin=1.22×10−210−7
θmin=1.22×10−7−(−2)
θmin=1.22×10−5 radians
Correct Answer
The correct option is (b) 1.22×10−5.
