Tag: the nature of light

Soft gamma rays, $x-$rays and microwaves are namely eletromagnetic having different wavelengths. 

We know that 
$\mu=\dfrac{V _{n}}{V _{m}}$

Speed of the light is constant with respect to any observer holds only for the vacuum. In different medium (say water) if observer is moving with respect to medium towards the source, the speed observed by the observer will be more compared to a stationary observer. 
Same thing holds for a observer moving away from the source. Hence Option A. 
Since they are moving at the same speed, change in speed will be same and hence Option D. 
So answer is A and D.

Relativity states that the speed of light in vacuum will be same independent of the frame of reference. The frame of reference can be stationary or moving.
So all  three will find the speed of light to be $ c $
Also $ c=\dfrac{1}{2}(c+c) $
So, (C) and (D) are correct.

Frequency remains constant during refraction.

$\displaystyle v _{med}=\dfrac{1}{\sqrt{\mu _0\epsilon _0\times4}}=\dfrac{c}{2}$

$\displaystyle\dfrac{\lambda _{med}}{\lambda _{air}}=\dfrac{v _{med}}{v _{air}}=\dfrac{\displaystyle\dfrac{c}{2}}{c}=\dfrac{1}{2}$

$\therefore$ wavelength is halved and frequency remains unchanged.

The electromagnetic waves of all wavelengths travel with the same speed in space which is equal to velocity of light.

Answer is B.

The apparent change in the wavelength is given as follows.
$\displaystyle \frac { \Delta \lambda  }{ \lambda  } =\frac { v }{ C } ,Hence\quad V=\frac { \Delta \lambda  }{ \lambda  } C$
$\displaystyle =\frac { 0.02 }{ 100 } \times 3\times { 10 }^{ 8 }{ ms }^{ -1 }=60{ kms }^{ -1 }$.
Hence, the velocity of the star is 60 km/s.