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My name is Ann [436]
3 years ago
8

Light containing two different wavelengths passes through a diffraction grating with 1,250 slits/cm. On a screen 17.5 cm from th

e grating, the third-order maximum of the shorter wavelength falls midway between the central maximum and the first side maximum for the longer wavelength. If the neighboring maxima of the longer wavelength are 8.44 mm apart on the screen, what are the wavelengths in the light
Physics
1 answer:
ki77a [65]3 years ago
5 0

Answer:

\lambda_s =6.43*10^-4m

Explanation:

From the question we are told that:

Diffraction grating N=1250slits/cm

Distance b/w Screen and grating length d_{sg}=17.5 cm

Distance b/w neighboring maxima and Screen d_{ms}=8.44

 

Generally the equation for grating space is mathematically given by

d(g)=\frac{1}{N}

d(g)=\frac{100}{1250}

d(g)=0.08

Generally the equation for small angle approximation is mathematically given by

\triangle y=\frac{\lambda d}{L}

Therefore for longest wavelength

\lambda _l=\frac{8.44*10^{-3}*(0.08)}{0.175m}

\lambda _l=3.858*10^{-3}

Therefore the third order maximum equation for the shorter wavelength as

\lambda_s =\frac{1}{6} \lambda_l

\lambda_s =\frac{1}{6} (3.858*10^-^3)

\lambda_s =6.43*10^-4m

The wavelengths in the light is given as

\lambda_s =6.43*10^-4m

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