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Lloyds Mirror. In Fig. 35-60, monochromatic light of

Chapter , Problem 104

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QUESTION:

Lloyds Mirror. In Fig. 35-60, monochromatic light of wavelength l diffracts through a narrow slit S in an otherwise opaque screen.On the other side,a plane mirror is perpendicular to the screen and a distance h from the slit. A viewing screen A is a distance much greater than h. (Because it sits in a plane through the focal point of the lens, screen A is effectively very distant. The lens plays no other role in the experiment and can otherwise be neglected.) Light that travels from the slit directly to A interferes with light from the slit that reflects from the mirror to A. The reflection causes a halfwavelength phase shift. (a) Is the fringe that corresponds to a zero path length difference bright or dark? Find expressions (like Eqs. 35-14 and 35-16) that locate (b) the bright fringes and (c) the dark fringes in the interference pattern. (Hint: Consider the image of S produced by the mirror as seen from a point on the viewing screen, and then consider Youngs two-slit interference.)

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QUESTION:

Lloyds Mirror. In Fig. 35-60, monochromatic light of wavelength l diffracts through a narrow slit S in an otherwise opaque screen.On the other side,a plane mirror is perpendicular to the screen and a distance h from the slit. A viewing screen A is a distance much greater than h. (Because it sits in a plane through the focal point of the lens, screen A is effectively very distant. The lens plays no other role in the experiment and can otherwise be neglected.) Light that travels from the slit directly to A interferes with light from the slit that reflects from the mirror to A. The reflection causes a halfwavelength phase shift. (a) Is the fringe that corresponds to a zero path length difference bright or dark? Find expressions (like Eqs. 35-14 and 35-16) that locate (b) the bright fringes and (c) the dark fringes in the interference pattern. (Hint: Consider the image of S produced by the mirror as seen from a point on the viewing screen, and then consider Youngs two-slit interference.)

ANSWER:

Problem 104

Lloyds Mirror. In Fig. 35-60, monochromatic light of wavelength  diffracts through a narrow-slit S in an otherwise opaque screen. On the other side, a plane mirror is perpendicular to the screen and a distance h from the slit. A viewing screen A is a distance much greater than h. (Because it sits in a plane through the focal point of the lens, screen A is effectively very distant. The lens plays no other role in the experiment and can otherwise be neglected.) Light that travels from the slit directly to A interferes with light from the slit that is reflected from the mirror to A. The reflection causes a half wavelength phase shift. (a) Is the fringe that corresponds to a zero-path length difference bright or dark? Find expressions (like Eqs. 35-14 and 35-16) that locate (b) the bright fringes and (c) the dark fringes in the interference pattern. (Hint: Consider the image of S produced by the mirror as seen from a point on the viewing screen, and then consider Young's two-slit interference.)

Fig. 35-60

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Step 1 of 3

Part (a)

The phenomenon in which more than two waves are superimposed to form a resultant wave is termed as interference. Whereas, in a double-slit experiment, the direct and the reflected ray from the mirror will combine and produce an interference pattern on the screen

Therefore, the reflected waves from a mirror have a phase difference of  that leads to the interchange of dark and bright fringes. Thus, the zero-path difference corresponds to a dark fringe.

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