State Which type of Media Ensures a light Propagation in form of Straight rays in Geometrical Optics: Physics Assignment, NUS, Singapore

Comprehension Questions (10 Points)

State which type of media ensures a light propagation in form of straight rays in geometrical optics.

a. State the law of refraction.

b. State the law of reflection.

c. Briefly explain what total internal reflection is.

d. Briefly explain what coherence is.

e. State what is described by the direction of the wave vector.

f. State how the wavelength of a wave changes when going from vacuum into a glass (n = 1.5).

g. State how the frequency of a wave changes when going from vacuum to glass (n = 1.5).

h. Briefly explain what a Newton black film is.

i. Briefly explain what Fraunhofer diffraction is.

Prism (7 Points)

The prism shown in Figure 1 is given.

a. Calculate the refractive index of a prism with angle α = 40^◦ (see Fig. 1a), where light incident perpendicular to the surface is deflected by an angle δ = 33.5^◦.

b. A ray with the wavelength 400 nm hits the same prism under the angle = 60^◦ (see Fig. 1b). For this wavelength the refractive index equals the one calculated in a) (If you do not get a result in a), use n_{400 nm} = 1.55). A second ray with the wavelength 700 nm hits the prism under the same angle. The refractive index here equals n_{700 nm} = n_{400 nm} − 0. Calculate the angle σ between the two rays leaving the prism.

Diver (2 Points)

A person is diving in the ocean (n = 1.33). While looking up he notices that he only can see the sky inside a ring with a radius of 5 m. Calculate how deep he is in the water.

Thin lenses (5 Points)

An object is placed 15 cm away from a thin lens with a focal length of f₁ = 6 cm.

a. Calculate the distance of the image with respect to the lens and the magnification. Is the image real or virtual? Is it upright or inverted?

b. A second lens with a focal length of f₂ = 4 cm is placed 16 cm behind lens 1. Calculate the distance between the object and the now resulting image. Calculate the total magnification. Is the image real or virtual? Is it upright or inverted?

Thick lens (3 Points)

A thick biconcave lens has a refractive index of n = 1.5 and radii of curvature of R₁ = −10 cm and R₂ = 8 cm. An object is placed 20 cm away from the lens.

a. Calculate the focal length of the lens,

b. the image distance,

c. and the magnification. Is the image real or virtual? Is it upright or inverted?

Telescope (5 Points)

a. Consider two biconvex lenses that have focal lengths of 75 mm and 25 mm and shall be used to build a telescope.

b. State which lens to use as the objective, which lens to use as the eyepiece, how far apart to place the lenses and what angular magnification you expect.

c. Draw a ray diagram to show how rays from a distant object are refracted by the two lenses.

Soap film (6 Points)

A planar soap water membrane appears in clear green colouration when observed by reflected light. The eye observes the membrane under an angle of α = 35^◦ (measured against the normal). Calculate the minimal thickness of the membrane and in which colour it appears when the eye looks from a perpendicular perspective (α = 0^◦). The soap water membrane has a refractive index of n = 1.33, and the wavelength of the green light is λ_gr = 500 nm. The following formula could come handy for reshaping equations: sin²(x) + cos²(x) = 1.

An anti-reflection coating (7 Points)

A microscope lens made of glass (n_g = 1.51) shall be coated with a layer to reduce reflections of light around 550 nm.

a. Calculate the optimal layer thickness when magnesium fluoride (n_s = 1.38) is used to enhance the transmission.

b. Calculate the residual reflectivity under perpendicular illumination.

c. Calculate the refractive index (for the wavelength λ) the coating should have to reduce the reflections under perpendicular illumination completely.

d. Justify why a coating with n_s > n_g at the same thickness would result in a higher reflectivity.

The reflection coefficient i.e. the reflectivity for the reflected intensity or perpendicular incidence of the light for the interface of a medium with n₁ an a medium with n₂ is given by:

A narrow single slit (in the air) in an opaque screen is illuminated by infrared light from a He-Ne laser at 1152.2 nm, and it is found that the centre of the tenth dark band in the Fraunhofer diffraction pattern lies at an angle of 6.4^◦ off the central axis.

a. Calculate the width of the slit.

b. Calculate the angle of the tenth minimum if the entire arrangement is immersed in water (n_w = 1.33) rather than air.

Diffraction grating (6 Points)

A parallel bundle of white light falls under a perpendicular angle on an optical line grating that has 100 lines per millimetre. With a convex lens with a focal length of 30 cm that is placed close to the grating a spectrum is created on an appropriately prepared screen. Calculate the relative distances on the screen

between the colours red and violet of the spectrum,

a. from the end of the spectrum in the first order to the beginning of spectrum in the second order.

b. The wavelength at the red limit of the spectrum is 760 nm and the violet limit is 400 nm.