A glass sheet measuring 13.5 cm × 22.0 cm is covered by a very thin opaque coati

Question

A glass sheet measuring 13.5 cm × 22.0 cm is covered by a very thin opaque coating. In the middle of this sheet is a thin, straight scratch 0.00150 mm thick, as shown in (Figure 1) . The sheet is totally immersed beneath the surface of a liquid having an index of refraction of 1.49. Monochromatic light strikes the sheet perpendicular to its surface and passes through the scratch. A screen is placed under water a distance 32.0 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? Express your answer in nanometers to three significant figures. Answer should be in NM.

Explanation / Answer

here,

thickness of scratch , d = 1.5 * 10^-6 m

screen distance , D = 0.32 m

y = 0.23 m

let the wavelength be lamda

y = n * lamda D/d

n = 1 ,

0.23 = lamda * 0.32 /( 1.5 * 10^-6)

lamda = 1.078 * 10^-6 m

refractive index of water , n = 1.33

wavelength of light in air , lamda' = lamda * n = 1.078 * 10^-6 * 1.33

lamda' = 1433.9 * 10^-9 m

lamda'= 1433.9 nm

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