# 4 optics problems

1. A 500 line/mm grating is illuminated by light with wavelength of 510 nm. How many bright fringes are seen on a screen that is 2 m wide located 2 m behind the grating?

2. An underwater diver sees the sun 50 degree above the horizontal. How high is the sub above the horizon to a fisherman in a boat directly above the diver?

3. You press two flat pieces of glass together so that a very thin layer of air is trapped between them. Incoming light can reflect from the boundary between the top glass plate and the air and the bottom plate.the two reflected waves can then interfere with each other. What is the smallest spacing between the plates that will produce a strong reflection when red light of 680 nm wavelength shines perpendicularly on them.

4. Two plane mirrors makes an angle of 58 degrees. A light ray enters the system and is reflected once off each mirror. Through what angle is the ray turned?

1. The separation of the grating elements is $d = 10^-3/500 m =2*10^-6 m$

the maximum angle of diffraction comes from $tan(\theta_{max}) = 2/2 =1$

$\theta_{max} = 45 degree$

The law that gives the number of maximum after diffraction as a function of the diffracting angle

$d*sin(\theta_{max})= k*\lambda$

where $\lambda$ is the wavelength and $k$ is the number of maximum

$k = d*sin(\theta_{max})/\lambda =2*10^-6*sin(45)/510*10^-9 =2.77$

hence the number of maximum seen on the screen is 2

2. The angle of the refraction of light at with the surface of the water from the water to the air (angle of light inside the water with the normal to the surface) is

$r = 90-50 =40 degree$

If i is the angle of the incidence of light from the air to the water (angle of light above the water with the normal to surface) then

$sin(i)/sin(r) = n$ where $n$ is the refractive index of water.

$sin(i)=n*sin(r) = 1.33*sin(40) = 0.85$

$i = 58.74 degree$

Hence the angle of light with the horizontal is

$\theta =90-58.74 = 31.25 degree$

3. the strong reflection happens when the difference of path between the two reflected waves is equal with the wavelength or a integer number of wavelengths. hence the correct answer is d (the last one)

$2*\lambda =2*680 =1360 nm$

4. The correct answer is 116 degree hence the correct choice is a) 120 degree.