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Although a photon has no rest mass, but ...

Although a photon has no rest mass, but it possesses the inertial mass `m="hf"/c^2` where h is Planck's constant , f is frequency of light and c is speed of light . Since light is deflected by a gravitational field , so it is naturally assured that photons have same gravitational behaviour as other particles. When photon is emitted from source of star of mass M and radius R, total energy of photon will be sum of hf and gravitational potential energy. At a large distance from star, the photon is beyond the star's gravitational field , so its gravitational potential energy becomes zero but its total energy remains constant. So frequency of a photon emitted from surface of a star decreases as it moves away from star. A photon in visible region of spectrum is thus shifted towards red end, and this phenomena is known as gravitational red shift.
The potential energy of photon which is at surface of star is (where , M=Mass of the star , R=Radius of the star, G=Universal gravitational constant )

A

hf

B

`(hf)/2`

C

`(GMhf)/(c^2R)`

D

`-(GMhf)/(c^2R)`

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Although a photon has no rest mass, but it possesses the inertial mass m="hf"/c^2 where h is Planck's constant , f is frequency of light and c is speed of light . Since light is deflected by a gravitational field , so it is naturally assured that photons have same gravitational behaviour as other particles. When photon is emitted from source of star of mass M and radius R, total energy of photon will be sum of hf and gravitational potential energy. At a large distance from star, the photon is beyond the star's gravitational field , so its gravitational potential energy becomes zero but its total energy remains constant. So frequency of a photon emitted from surface of a star decreases as it moves away from star. A photon in visible region of spectrum is thus shifted towards red end, and this phenomena is known as gravitational red shift. If f' is frequency of photon when it is very far away from star then (f-f')/f

Although a photon has no rest mass, but it possesses the inertial mass m="hf"/c^2 where h is Planck's constant , f is frequency of light and c is speed of light . Since light is deflected by a gravitational field , so it is naturally assured that photons have same gravitational behaviour as other particles. When photon is emitted from source of star of mass M and radius R, total energy of photon will be sum of hf and gravitational potential energy. At a large distance from star, the photon is beyond the star's gravitational field , so its gravitational potential energy becomes zero but its total energy remains constant. So frequency of a photon emitted from surface of a star decreases as it moves away from star. A photon in visible region of spectrum is thus shifted towards red end, and this phenomena is known as gravitational red shift. If a photon of original frequency f falls through a small height H near the earth's surface, then fractional charge in frequency will be (acceleration due to gravity is g)

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