Concepts Of Physics MCQ Edition [Volume 1]PhysicsLight Waves
A parallel beam of light of wavelength 620 nm is focused by a convex lens of diameter 8.0 cm . Determine the diameter of the central bright spot formed if the light is focused at a distance of 20 cm from the lens.
Options
- A3.8 10⁻⁶ m
- B7.6 10⁻⁶ m
- C4.8 10⁻⁶ m
- D1.9 10⁻⁶ m
Correct answer
A. 3.8 10⁻⁶ m
Step-by-step solution
Given: Wavelength of light, = 620 nm = 620 10⁻⁹ m Diameter of the lens, D = 8.0 cm = 8.0 10⁻² m Focal length of the lens, f = 20 cm = 20 10⁻² m The radius of the central bright spot (Airy disk) formed by a lens is given by: r = 1.22 f D The diameter of the central bright spot is: d = 2r = 2.44 f D Substituting the given values: d = 2.44 620 10⁻⁹ 20 10⁻² 8.0 10⁻² d = 2.44 620 10⁻⁹ 20 8.0 d = 2.44 1550 10⁻⁹ m d = 3782 10⁻⁹ m d = 3.782 10⁻⁶ m Rounding to two significant figures, we get: d 3.8 10⁻⁶ m