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You illuminate a slit with a width of 77.7 μm with a light of wavelength 721 nm and observe the resulting diffraction pattern on a screen th
Question
You illuminate a slit with a width of 77.7 μm with a light of wavelength 721 nm and observe the resulting diffraction pattern on a screen that is situated 2.83 m from the slit. What is the width, in centimeters, of the pattern’s central maximum
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Physics
3 years
2021-08-21T04:36:31+00:00
2021-08-21T04:36:31+00:00 1 Answers
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Answer:
The width is![Rendered by QuickLaTeX.com Z = 0.0424 \ m](https://documen.tv/wp-content/ql-cache/quicklatex.com-eb72c38b983f2dc02fcccca473c93f01_l3.png)
Explanation:
From the question we are told that
The width of the slit is![Rendered by QuickLaTeX.com d = 77.7 \mu m = 77.7 *10^{-6} \ m](https://documen.tv/wp-content/ql-cache/quicklatex.com-91bebbbb41ee35811ef536919293b2db_l3.png)
The wavelength of the light is![Rendered by QuickLaTeX.com \lambda = 721 \ nm](https://documen.tv/wp-content/ql-cache/quicklatex.com-d4a340bda5b659eedb830d7e513f5aca_l3.png)
The position of the screen is![Rendered by QuickLaTeX.com D = 2.83 \ m](https://documen.tv/wp-content/ql-cache/quicklatex.com-15a328b73690730066ab785dc186584b_l3.png)
Generally angle at which the first minimum of the interference pattern the light occurs is mathematically represented as
Where m which is the order of the interference is 1
substituting values
Now the width of first minimum of the interference pattern is mathematically evaluated as
substituting values
Now the width of the pattern’s central maximum is mathematically evaluated as
substituting values