Tag: theories on light

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Questions Related to theories on light

Multiple choice physics wave optics huygens wave theory and wavefront wave propagation (huygens' construction) theories on light wave behaviour

The wavefront of a lightbeam is given by the equation $x+2y+3z=c$,(where c is arbitary constant) the angle made by the direction of light with the y-axis is:

  1. ${ cos }^{ -1 }\frac { 1 }{ \sqrt { 14 } } $
  2. ${ cos }^{ -1 }\frac { 2 }{ \sqrt { 14 } } $
  3. ${ sin }^{ -1 }\frac { 1 }{ \sqrt { 14 } } $
  4. ${ sin }^{ -1 }\frac { 2 }{ \sqrt { 14 } } $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given,

Direction of light, $\vec n=\hat i+2\hat j+3\hat k$
The angle made by the direction of light with y-axis is
$cos\beta=\hat n.\hat j$
$cos\beta=\dfrac{\vec n}{|\vec n|}.\hat j$
$cos\beta=\dfrac{(\hat i+2\hat j+3\hat k).(0\hat i+\hat j+0\hat k)}{\sqrt{(1)^2+(2)^2+(3)^2}}=\dfrac{2}{\sqrt{14}}$
$\beta=cos^{-1}\dfrac{2}{\sqrt{14}}$
The correct option is B.

Multiple choice physics wave optics huygens wave theory and wavefront wave propagation (huygens' construction) theories on light wave behaviour

The two coherent sources of equal intensity produce maximum intensity of $100$ units at a point. If the intensity of one of the sources is reduced by $50\%$ by reducing its width then the intensity of light at the same point will be

  1. 90

  2. 81

  3. 67

  4. 72.85
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Maximum intensity I_max is proportional to (a1 + a2)^2 = 100 units, meaning a1 + a2 = 10. Reducing the width of one source by 50% reduces its amplitude by a factor of sqrt(0.5). Solving for the new amplitudes and calculating the new maximum intensity via (a1 + a_new)^2 yields approximately 72.85 units.

Multiple choice physics wave optics huygens wave theory and wavefront wave propagation (huygens' construction) theories on light wave behaviour

 For what distance ray optics a good approximation when the aperture is 4 mm wide and the wavelength is 500nm?

  1. $32m$
  2. $69 m$
  3. $16 m$
  4. $8 m$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
The Good approximation distance till ray optics or valid is given by Fresnel distance which is given by
$z _f=\dfrac{a^2}{\lambda}$
$z _f$ is distance till which diffraction effects of light can be neglected.
$a=$ aperature$=4\times 10^{-3}m$
$\lambda =$wavelength$=500\times 10^{-9}$m
$z _f=\dfrac{(4\times 10^{-3})^2}{(500\times 10^{-9})m}$
$=\dfrac{16\times 10^{-6}}{500\times 10^{-9}}$
$=0.032\times 10^3$m
$\therefore z _f=32m$.
Multiple choice physics wave optics huygens wave theory and wavefront wave propagation (huygens' construction) theories on light wave behaviour

At the first minimum adjacent to the central maximum of a single slit diffraction plate the phase difference between the huygens wavelet from the edge of the slit and the wavelet from the midpoint of the slate

  1. $\pi/8$
  2. $\pi/4$
  3. $\pi/2$
  4. $\pi$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

At the first minimum, the path difference between the edges of the slit is lambda. The path difference between the edge and the midpoint is lambda/2, which corresponds to a phase difference of pi.

Multiple choice physics wave optics huygens wave theory and wavefront wave propagation (huygens' construction) theories on light wave behaviour

If light waves emitted by an ordinary source, for what period of time, the phase remains constant :-

  1. $10 sec$
  2. $1 sec$
  3. $10^{-3}$ sec
  4. $10^{-8}$ sec
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In ordinary light sources, light is emitted due to independent atomic transitions lasting roughly 10^-8 seconds, during which the phase remains relatively constant before a sudden random phase change occurs.