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Homework Assignment 04

The document is a homework assignment for an Advanced Optics course, focusing on concepts of diffraction including Fresnel and Fraunhofer diffraction, as well as calculations related to slit width and angles of diffraction. It includes various problems requiring the application of formulas and phasor diagrams to analyze diffraction patterns and intensity. Specific tasks involve calculating slit dimensions, angles, and the number of lines in diffraction gratings based on given wavelengths and angles.

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Bimsara Wickramasinghe
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48 views2 pages

Homework Assignment 04

The document is a homework assignment for an Advanced Optics course, focusing on concepts of diffraction including Fresnel and Fraunhofer diffraction, as well as calculations related to slit width and angles of diffraction. It includes various problems requiring the application of formulas and phasor diagrams to analyze diffraction patterns and intensity. Specific tasks involve calculating slit dimensions, angles, and the number of lines in diffraction gratings based on given wavelengths and angles.

Uploaded by

Bimsara Wickramasinghe
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Advanced Optics

PH 4012

Homework Assignment 04

(01)What do you mean by diffraction? What are the major differences


between Fresnel diffraction and Fraunhofer diffraction?

(02)How does diffraction differ from interference?

(03)In Fraunhofer diffraction, white light falls on a slit of width ‘a’.


Calculate the value of ‘a’ for which the first minimum of red light
(𝜆 = 6500 𝐴0 ) falls at 30o. Also find the wavelength of light
whose first diffraction maximum coincides with the first minimum
of red light.

(04)Monochromatic light of wavelength 441 nm falls on a narrow slit


in a Fraunhofer diffraction experiment. The screen is placed 2.16
m away. The distance between the second minimum and the
central maximum is 1.62 cm. Calculate
(a) The angle of diffraction 𝜃 for second minimum
(b) The width of the slit ‘a’

(05)Using a phasor diagram show that the intensity at a point in


Fraunhofer’s diffraction due to ingle slit is given by

sin 𝛼 2 𝜋
𝐼= 𝐼𝑜 ( 𝛼 ) , 𝛼 = 𝜆 𝑎 𝑠𝑖𝑛𝜃

Where the symbols have their usual meanings


(06)Using suitable phasor diagrams show that the intensity (𝐼)at an
angle of 𝜃 incident on a screen placed far away from the grating
with N slits is given by

sin 𝛼 2 sin 𝑁𝛽 2 𝜋
𝐼 = 𝐼𝑜 ( ) ( sin 𝛽 ) , 𝛽= (𝑎 + 𝑏) 𝑠𝑖𝑛𝜃
𝛼 𝜆

Where the symbols have their usual meanings

(07)How many lines per cm are there in a grating which gives an


angle of diffraction of 600 in the first order of light of
wavelength 5 × 10−5 𝑐𝑚?

(08)A diffraction grating has a total ruled width 5cm. It is found that
for normal incidence, a spectral line of wavelength 500 nm in a
certain order superimposes on another spectral line of
wavelength 550 nm of the next higher order. If the angle of
diffraction is 25o, what is the total number of lines on the grating

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