A diffraction grating has 5000 lines per cm. The angle between the central maximum and the first order maximum is 11.8e. What is the wavelength of the light? A) 183 nm B) 409 nm C)...

A diffraction grating has 5000 lines per cm. The angle between the central maximum and the first order maximum is 11.8e. What is the wavelength of the light?

A) 183 nm B) 409 nm C) 138 nm D) 637 nm

Light of wavelength 580 nm is incident on a slit of width 0.300 mm. An observing screen is placed 2.00 m from the slit. Find the position of the first order dark fringe from the center of the screen.
A) 3.9 mm B) 1.9 mm C) 0.26 mm D) 7.7 mm
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1 Answer
The equation necessary to solve this problem is:
m`` =dsin``
In this problem m is equal to 1 as we have been given the angle of the first order maximum: ``
The above equation is then simplified to: `` =dsin``
In order to calculate the slit spacing, d, we divide 1 cm by the diffraction gradient: d = 1/5000 = 0.0002 cm.
In order to simplify the conversion of the wavelength units to nanometers (nm), this spacing is converted to a unit of meters: d = 0.0002/100 = 2.0x10^6 m
Substituting the known parameters into the equation for `` we get:
= (2.0x10^6)sin(11.8) = 4.09x10^7 m = 409 nm
Therefore, the correct answer to this question is B) 409 nm.
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