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Monochromatic light of wavelength 530 nm passes through a horizontal single slit of width 1.5μm in an opaque plate. A screen of dimensions 2.0m×2.0m is 1.2 m away from the slit.

(a) Which way is the diffraction pattern spread out on the screen?
(b) What are the angles of the minima with respect to the center?
(c) What are the angles of the maxima?
(d) How wide is the central bright fringe on the screen?
(e) How wide is the next bright fringe on the screen?

1 Answer

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Final answer:

The diffraction pattern is spread out horizontally on the screen. The angles of the minima and maxima can be determined using formulas involving the wavelength of light and the width of the slit. The width of the central bright fringe and the next bright fringe can be determined using formulas involving the wavelength of light, the distance between the slit and the screen, the width of the screen, and the angle of the first minimum.

Step-by-step explanation:

(a) The diffraction pattern is spread out horizontally on the screen.

(b) The angles of the minima with respect to the center can be determined using the formula sin(theta) = (m * lambda) / w, where m is the order of the minimum, lambda is the wavelength of light, and w is the width of the slit. In this case, for the first minimum (m = 1), the angle is sin(theta) = (1 * 530 nm) / 1.5 um.

(c) The angles of the maxima can be determined using the formula sin(theta) = (m * lambda) / w, where m is the order of the maximum. In this case, for the first maximum (m = 1), the angle is sin(theta) = (1 * 530 nm) / 1.5 um.

(d) The width of the central bright fringe can be determined using the formula w = (2 * lambda * D) / W, where lambda is the wavelength of light, D is the distance between the slit and the screen, and W is the width of the screen. In this case, the width of the central bright fringe is w = (2 * 530 nm * 1.2 m) / 2.0 m.

(e) The width of the next bright fringe can be determined using the formula w = (lambda * D) / (W * sin(theta)), where lambda is the wavelength of light, D is the distance between the slit and the screen, W is the width of the screen, and theta is the angle of the first minimum. In this case, the width of the next bright fringe is w = (530 nm * 1.2 m) / (2.0 m * sin(theta)).

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