A glass sheet measuring 11.0 cm × 24.0 cm is covered by a very thin opaque coati

Question

A glass sheet measuring 11.0 cm × 24.0 cm is covered by a very thin opaque coating. In the middle of this sheet is a thin, straight scratch 1.05×10?3 mmthick, as shown in the figure (Figure 1) . The sheet is totally immersed beneath the surface of a liquid having an index of refraction of 1.47. Monochromatic light strikes the sheet perpendicular to its surface and passes through the scratch. A screen is placed under water a distance 37.0 cm away from the sheet and parallel to it. You observe that the first dark fringes on either side of the central bright fringe on this screen are 22.8 cm apart.

Explanation / Answer

The liquid reduces the wavlength of the light (compared to its value in air), and the scratch causes light passing through it to undergo single-slit diffraction.

Sin A = lambda/a

lambda is wavelength in liquid

n = lambda)air/lambda

tan A = (22.8/2)/37

A = arctan(22.8/74) = 17.12 deg

lambda = a*sin A = 1.05*10^-6*sin 17.12 deg = 3.091*10^-7 m

lambda = 309.1 nm

n = 1.47

lambda)air = n*lambda = 1.47*309.1 nm = 454.38 nm

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