The ratio of the intensities at minima to maxima in the interference pattern is 9 : 25. What will be the ratio of the widths of the two slits in the Young's double-slit experiment?

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Solution

Given,
Ratio of intensities at minima to maxima = 9:25

Intensity is proportional to width of slit.

So, amplitude a₁ and a₂ is proportional to the square root of the width of the slit.

∴

\frac{a_{1}}{a_{2}} = \sqrt{\frac{ω_{1}}{ω_{2}}}

Here

ω_{1}

and

ω_{2}

represent the widths of the two slits.

Now, we have

\frac{I_{\min}}{I_{\max}} = \frac{(a_{1} - a_{2})^{2}}{(a_{1} + a_{2})^{2}} = \frac{{(1 - \frac{a_{2}}{a_{1}})}^{2}}{{(1 + \frac{a_{2}}{a_{1}})}^{2}}

\frac{9}{25} = \frac{{(1 - \frac{a_{2}}{a_{1}})}^{2}}{{(1 + \frac{a_{2}}{a_{1}})}^{2}} \Rightarrow \frac{3}{5} = \frac{1 - \frac{a_{2}}{a_{1}}}{1 + \frac{a_{2}}{a_{1}}}

\Rightarrow

8 \frac{a_{2}}{a_{1}} = 2

\Rightarrow

\frac{a_{1}}{a_{2}} = 4

Thus,

\sqrt{\frac{ω_{1}}{ω_{2}}} = \frac{4}{1}

i.e.,

\frac{ω_{1}}{ω_{2}} = \frac{16}{1} \Rightarrow ω_{1} : ω_{2} = 16 : 1 .

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Wave Optics

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For Daily Free Study Material Join wiredfaculty

Wave Optics

The ratio of the intensities at minima to maxima in the interference pattern is 9 : 25. What will be the ratio of the widths of the two slits in the Young's double-slit experiment?

Some More Questions From Wave Optics Chapter

What is the shape of the wavefront in each of the following cases:The portion of the wavefront of light from a distant star intercepted by the Earth.

Is the speed of light in glass independent of the colour of light? If not, which of the two colours red and violet travels slower in a glass prism?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

What is the shape of the wavefront in each of the following cases:
The portion of the wavefront of light from a distant star intercepted by the Earth.