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Two coherent sources of intensity ratio 25 ∶ 9 are used in an interference experiment. The ratio of intensities of maxima and minima in the interference pattern is:  


1. 25 ∶ 16
2. 49 ∶ 4
3. 64 ∶ 4
4. 8 ∶ 3

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Correct Answer - Option 3 : 64 ∶ 4

Concept:

  • Coherent sources of light: Two narrow sources of light are said to be coherent if they emit waves having:

    • The same wavelength (or frequency)
    • The same amplitude
    • constant phase relation between them
  • Interference: It is the phenomenon of the superimposition of waves. 
    • Conditions required for producing sustained interference:
      • The two sources of light must be coherent.
      • The sources must be monochromatic (i.e. of a single wavelength).
      • For better contrast between maxima and minima of intensity, the amplitudes of the interfering waves should be equal.

The intensity of the light ∝  width of the slit (W)

\(\frac{{{W_1}}}{{{W_2}}} = \frac{{{I_1}}}{{{I_2}}}\)

Intensity ∝ square of the amplitude

\(\frac{{{W_1}}}{{{W_2}}} = \frac{{{I_1}}}{{{I_2}}} = \frac{{a_1^2}}{{a_2^2}}\)

\( \frac{{{I_{max}}}}{{{I_{min}}}} = \frac{{{{\left( {{a_1} + {a_2}} \right)}^2}}}{{{{\left( {{a_1} - {a_2}} \right)}^2}}} \)

Calculation:

Given that, I= 25, I2 = 9

\(\frac{{{I_1}}}{{{I_2}}} = \frac{{25}}{9}\)

\(\begin{array}{l} \frac{{{I_1}}}{{{I_2}}} = \frac{{a_1^2}}{{a_2^2}} = \frac{{25}}{9}\Rightarrow \frac{{{a_1}}}{{{a_2}}} = \frac{5}{3} \end{array}\)

\(\begin{array}{l} \frac{{{I_{max}}}}{{{I_{min}}}} = \frac{{{{\left( {{a_1} + {a_2}} \right)}^2}}}{{{{\left( {{a_1} - {a_2}} \right)}^2}}} = \frac{{{{\left( {\frac{{{a_1}}}{{{a_2}}} + 1} \right)}^2}}}{{{{\left( {\frac{{{a_1}}}{{{a_2}}} - 1} \right)}^2}}} = \frac{{{{\left( {\frac{5}{3} + 1} \right)}^2}}}{{{{\left( {\frac{5}{3} - 1} \right)}^2}}} = {\left( {\frac{8}{2}} \right)^2} = \frac{64}{4} \end{array}\)

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