Question

(a) A monochromatic laser light of blue color with a wavelength of exactly 450 nm is flashed directly upwards from ground floor. Someone on the 15th floor, at a height of 50 m receives it. What wavelength they would find this light to have? 

(b) A Neutron star is a very compact object with mass equal to about the mass of the sun compressed within a radius of 10 km. They are routinely observed as pulsars in the sky. Suppose the same experiment as in part a is repeated from the surface of a Neutron star. What would be the wavelength now at a height of 50 m? Would it induce a noticeable color change?

Answer 1

We are given that, 

Wavelength of blue light = λ = 450 nm = 450 × 10⁻⁹ m 

Height of 15th floor = h = 50 m. 

We want to calculate wavelength of light at 15th floor. 

(a) As we know that while going up photon’s angular frequency changes that can be calculated by using the equation,

So a person on 15 floor would find approximately same wavelength of light. 

(b) Now we are given that, Mass of Neutron star = Mass of Sun = Ms = 2 × 10³⁰ m 

Radius of Neutron star = R = 10 km = 10⁴ m.

Again wavelength at the height of 50 m can be calculated by using equation,

= 0.333 nm. 

Since wavelength change is very small a color change may not occur.