9. [15 points] Consider a Young's double slit experiment, with two long parallel identical slits distance d apart. The width of the slits are narrow enough for the diffraction effects to be negligible. A laser of wavelength A is incident normally on the slits, forming interference pattern. on a distant screen. The experimenter covers one of the slits with a thin film of thickness t made of transparent material of refractive index n. The setup is shown in the figure below. (a) Before one slit is covered by the thin film, the central bright fringe is indeed at the center (0 = 0 with respect to the original direction of the laser beam). After the slit is covered, at what angle is this central fringe shifted to?
9. [15 points] Consider a Young's double slit experiment, with two long parallel identical slits distance d apart. The width of the slits are narrow enough for the diffraction effects to be negligible. A laser of wavelength A is incident normally on the slits, forming interference pattern. on a distant screen. The experimenter covers one of the slits with a thin film of thickness t made of transparent material of refractive index n. The setup is shown in the figure below. (a) Before one slit is covered by the thin film, the central bright fringe is indeed at the center (0 = 0 with respect to the original direction of the laser beam). After the slit is covered, at what angle is this central fringe shifted to?
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![9. [15 points] Consider a Young's double slit experiment, with two long parallel identical slits
distance d apart. The width of the slits are narrow enough for the diffraction effects to be
negligible. A laser of wavelength A is incident normally on the slits, forming interference pattern
on a distant screen. The experimenter covers one of the slits with a thin film of thickness t
made of transparent material of refractive index n. The setup is shown in the figure below.
(a) Before one slit is covered by the thin film, the central bright fringe is indeed at the center
(0 = 0 with respect to the original direction of the laser beam). After the slit is covered,
at what angle is this central fringe shifted to?
S₁
n S₂
0
(b) What is the smallest value of t such that there is a bright fringe present at the central
position after a slit is covered?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5e7f421-4fd8-49d8-b638-131a56945312%2F1f0dd317-aa17-41ea-bda7-aa8c7b549f53%2F029z7dx_processed.png&w=3840&q=75)
Transcribed Image Text:9. [15 points] Consider a Young's double slit experiment, with two long parallel identical slits
distance d apart. The width of the slits are narrow enough for the diffraction effects to be
negligible. A laser of wavelength A is incident normally on the slits, forming interference pattern
on a distant screen. The experimenter covers one of the slits with a thin film of thickness t
made of transparent material of refractive index n. The setup is shown in the figure below.
(a) Before one slit is covered by the thin film, the central bright fringe is indeed at the center
(0 = 0 with respect to the original direction of the laser beam). After the slit is covered,
at what angle is this central fringe shifted to?
S₁
n S₂
0
(b) What is the smallest value of t such that there is a bright fringe present at the central
position after a slit is covered?
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