A glass sheet measuring 15.0 cm x 30.0 cm is covered by a very thin opaque coati

Question

A glass sheet measuring 15.0 cm x 30.0 cm is covered by a very thin opaque coating. In the middle of this sheet is a thin, straight scratch 0.00110 mm thick, as shown in (Figure 1). The sheet is totally immersed beneath the surface of a liquid having an index of refraction of 1.44. Monochromatic light strikes the sheet perpendicular to its surface and passes through the scratch. A screen is placed under water a distance 31.0 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 23.0 cm apart. What is the wavelength of the light in air?

Explanation / Answer

Sin A = Lambda / a

lambda = wavelength in liquid

n = lambda_air / lambda

Tan A =( 23/2) /31 = arcTan(23/62) = 20.35 deg

lambda = a ( Sin A ) = 1.1*10^-6( Sin 20.35 deg) = 0.382* 10^-6 m

n = 1.44

lambda_air = n*lambda = 1.44 * 0.382*10^-6 = 550.08 nm

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