Question:

The $6563 \,?$ $H_\alpha$ line emitted by hydrogen in a star is found to be red-shifted by $15\,?$. The speed with which the star is receding from the earth is

Updated On: Jul 7, 2022

$3.2\times 10^{5} ms^{-1}$
$6.87\times 10^{5} ms^{-1}$
$2\times 10^{5} ms^{-1}$
$12.74\times 10^{5} ms^{-1}$

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The Correct Option is B

Solution and Explanation

Wavelength of $H_{\alpha}$ line, $\lambda = 6563 ? $ $= 6563 \times 10^{-10} m$ Red shift observed in star, $\left(\lambda' -\lambda\right) =15? $ $= 15 \times 10^{-10} m$ Let the velocity of the star with which it is receding away from the earth be $v$ $\therefore$ Red shift relation, $\lambda' - \lambda = \frac{v}{c} \lambda$ $\therefore v = \frac{c}{\lambda} \times\left(\lambda' -\lambda\right)$ $ = \frac{3\times 10^{8}\times 15\times 10^{-10}}{6563\times 10^{-10}}$ $= 6.86 \times 10^{5} ms^{-1}$

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Notes on huygens principle

Concepts Used:

Huygen's Principle

The principle that states, that each point of the wavefront is the source of the secondary wavelets, it spreads out in all directions with the speed of a wave is the Huygens Principle. According to Huygens’ principle, as the wavefronts will be in the forward direction, all the points on the wavefront will become a secondary source. All the secondary sources emit wavelets and tangents and are drawn to all the wavelets which is the new position of the waveform.

Over and above that Huygen’s Principle, is known as the Huygens–Fresnel Principle. These are the following features of wave propagation:

Every secondary source forms its own wavelets which are akin to the primary source.
Randomly, at any point, the tangents in the forward direction form a new wavefront.
The total of all the spherical wavelets is the wavefront.

Advantages and Disadvantages of the Huygens Principle:

Advantages:

The reflection and refraction of light are also proved with the help of Huygens' concept.
The concepts like diffraction of light, as well as interference of light, were also proved by Huygens'.

Disadvantage:

Huygens's principle has not discussed or proved the concepts like emission of light, absorption of light, and the polarization of light.
Huygens' principle fails the explanation of the photoelectric effect.
A serious drawback is that the theory advances an all-pervading medium required to propagate light called luminiferous ether. This was proved to be false in the twentieth (20^th) century.