Some distant star is to be observed by some telescope of diameter of objective lens a , at an angular resolution of 3.0 10⁻⁷ radian. If the wavelength of light from the star reaching the telescope is 500 nm, the minimum diameter of the objective lens of the telescope is ________ cm. (nearest integer)

Step-by-step solution

The angular resolution of a telescope is given by the formula: = 1.22 a where is the wavelength of light and a is the diameter of the objective lens. Given: = 3.0 10⁻⁷ rad = 500 nm = 500 10⁻⁹ m = 5 10⁻⁷ m Substituting the values into the formula: 3.0 10⁻⁷ = 1.22 5 10⁻⁷ a a = 1.22 5 10⁻⁷ 3.0 10⁻⁷ a = 6.1 3.0 m a = 2.0333... m Converting the diameter into centimeters: a = 2.0333... 100 cm = 203.33 cm Rounding to the nearest integer, we get 203 cm. Answer: 203