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.

Step-by-step solution

The limit of resolution of a telescope is given by the formula: = 1.22 R where is the wavelength of light and R is the diameter of the objective lens. Given: = 500 nm = 500 10⁻⁹ m = 5 10⁻⁷ m = 5 10⁻⁷ rad Substituting the values into the formula: 5 10⁻⁷ = 1.22 5 10⁻⁷ R R = 1.22 m Converting to centimeters: R = 1.22 100 cm = 122 cm Answer: 122