Choose two problems from the following: The focal length of a regular lens in a
ID: 1519429 • Letter: C
Question
Choose two problems from the following: The focal length of a regular lens in a camera is 50 mm. An object of height 10 cm is 0.6 m in front of the camera, and its image is sharply formed on the film in the camera. Estimate the distance between the film and the lens, and the height of the image on the film. Draw a ray diagram for the image on the film, and explain all the optical properties of the image. Find the thinnest oil film of refractive index 1.52 on the surface of water for which constructive interference for a red light of vacuum wavelength 632.8 nm takes place by reflection. What is the thinnest (non-zero) thickness when the film appears dark? (Assume the light beam incident to the film perpendicularly and the index of refraction for soap water is n = 1.33) Monochromatic light of wave length 450 nm is incident perpendicularly on a grating that is 5.0 mm wide ruled 2,400 lines. Find the angle of diffraction for the second order fringe. What is the highest order fringe in the diffraction pattern?Explanation / Answer
E) Here, 1/v = 1/5 - 1/60
=> v = 5.45 cm
=> distance between film and lens = 5.45 cm
=> height of image = (5.45/60) * 10
= 0.908 cm
F) For constructive interference
=> oil film thickness = [(2m + 1)/2] * (lambda/2n)
= (1/2) * (632.8)/(2 * 1.52)
= 104.07 nm
For film appearing dark
=> oil film thickness = [m] * (lambda/2n)
= (1) * (632.8)/(2 * 1.52)
= 208.15 nm
G) Here, d * sin(theta) = n * lambda
=> 2.083 * 10-6 * sin(theta) = 2 * 450 * 10-9
=> angle of diffraction = 25.6 degree
=> highest order fringe = 2.083 * 10-6 * sin(90)/450 * 10-9
= 4
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