Refractive index and Snell's law

The diagram shows a ray of light passing from medium X to medium Y to medium Z. The speed of light in medium X is v_X, the speed of light in medium Y is v_Y and the speed of light in medium Z is v_Z.

Which of the following shows the speeds in order of increasing magnitude?

Light travelling in glass of refractive index n_g is incident at a boundary with water of refractive index n_w. The critical angle for the boundary is C. Which of the following expressions is correct for this boundary?

A simple astronomical refracting telescope consists of two converging lenses. Light from a star is brought to a focus by the objective lens and then viewed through an eyepiece lens as shown.

In the arrangement shown, the final image is formed at infinity.

Explain why the separation of the objective and eyepiece lenses is equal to the sum of their focal lengths.

State why the final image is inverted.

Glass lenses used for optical instruments often have an anti-reflective coating. The coating is a thin layer of a transparent substance with refractive index n_c. Light is reflected from the coating surface and from the lens surface as shown. The reflected light interferes destructively.

When a single-layer coating is used, the coating thickness is chosen to eliminate reflections for green light, which is in the middle of the visible spectrum.

Calculate the minimum thickness d of the coating required for the reflection of green light to be eliminated.

frequency of green light = 6.00 10¹⁴Hz

State why white light reflected from coated lenses is seen as purple.

The lens in the eye of an octopus focuses light onto the retina at the back of the eye.

The octopus focuses on objects at different distances from the eye by changing the shape of the eye to move the lens closer or further from the retina.

The power of an octopus lens is 118 D.

Show that the focal length of the lens is about 8.5 mm.

Calculate the shortest distance from the eye at which an object may be focused clearly on the retina.

maximum distance from lens to retina = 2.0 cm

The lens in the eye of an octopus is in contact with seawater. The refractive index of freshwater is less than the refractive index of seawater.

Deduce what would happen to the shortest distance from the eye at which an object may be focused clearly if the octopus was in freshwater.

Calculate the speed of light in seawater.

refractive index of seawater = 1.37

An octopus can detect the orientation of polarised light.

State what is meant by polarised light.

The angle of incidence of the light as it enters the tank is 7.2°

Show that the refractive index of the liquid is about 1.4

w = 35.0 cm t = 4.0 cm s = 10.2 cm

Determine the speed of light in the liquid.

The angle of incidence of the light as it enters the tank is 7.2°

Show that the refractive index of the liquid is about 1.4

w = 35.0 cm t = 4.0 cm s = 10.2 cm

Determine the speed of light in the liquid.

Light entering a normal eye is refracted by both the cornea and the lens before a focused image is formed on the retina.

It is suggested that the cornea provides 80% of the focusing power of the eye.

Determine whether this is correct.

focal length of cornea = 2.23 cm

focal length of lens for near object = 5.27 cm

Light from a point object forms a focused image on the retina.

The cornea and lens may be treated as a single lens of focal length 1.6 cm that is 2.4 cm from the retina.

Calculate the distance from the point object to this single lens when a focused image is formed on the retina.

A ray of light strikes the front of the cornea at an angle to the normal in air of 15.

Calculate the angle of the ray to the normal in the cornea.

speed of light in air = 3.0010⁸m s^–1

speed of light in cornea = 2.1810⁸m s^–1

People swimming under water often wear goggles. The goggles enable them to see objects under water clearly whereas without goggles objects appear blurred.

Explain why wearing goggles has this effect.

speed of light in water = 2.2510⁸m s^–1