Lenses

The closest distance from the eye where light from an object can be brought to a focus is known as the near point distance. The near point distance for a human eye is taken to be 25 cm.

A long‑sighted eye has a near point distance greater than 25 cm. This may cause problems with focusing on near objects.

A converging lens can be used to correct this problem. The converging lens forms an image of a near object at the actual near point distance of the long‑sighted eye.

State the type of image formed by the converging lens when used to correct a long‑sighted eye.

The near point distance for a long‑sighted eye is 65 cm.

Calculate the power, in dioptres, of the converging lens required.

A diverging lens can also be used to correct problems with eyesight.

Draw a ray diagram on the axes below to show the formation of the image of a distant object by a diverging lens. F marks the position of each principal focus of the lens.

A student used two converging thin lenses in combination to form an image of an object.

Show that the power of the combination of lenses was about 20 D.

focal length of lens 1 = 10 cm focal length of lens 2 = 15 cm

The object was 4 cm in front of the combination of lenses.

Calculate the image distance.

The object height was 1.4 cm.

Calculate the image height.

The object is magnified.

State two other properties of the image.

Galileo is credited with inventing the first telescope in 1610. The picture shows an early demonstration of the telescope.

(Source: © CPA Media Pte Ltd/Alamy Stock Photo)

A converging lens was positioned at one end of the telescope. A diverging lens was placed at the other end and a person looked through this lens.

The converging lens produced an image at a distance equal to the focal length of the lens.

Explain what can be concluded about the object being viewed.

The final image produced by the telescope is described as virtual and upright.

State what is meant by virtual and upright.

Virtual

Upright

The image, I, produced by the converging lens is at a distance from the diverging lens equal to the focal length of the diverging lens, as shown. This image acts as an object for the diverging lens.

The distance equal to the focal length on the other side of the lens is marked with F.

Draw the ray diagram for the diverging lens.

Galileo’s first telescope had a magnification of 10, and a distance between the centres of the two lenses of 90 cm.

Calculate the focal length of each lens.

Galileo was the first person to observe Jupiter’s larger moons.

Ganymede is Jupiter’s largest moon. The distance between the centre of Ganymede and the centre of Jupiter is 1.07×10⁶km. Ganymede takes 171 hours to complete an orbit around Jupiter.

Calculate the mass of Jupiter.

The focal length and power of a converging glass lens are determined for the lens in air. The lens is then immersed in water.

Which row in the table shows how the focal length and power of the lens change?

The lens of a mobile phone camera has a focal length of 4.25 mm. Light is focused onto light sensors at the back of the camera, as shown.

The camera is initially focused on an object in the far distance.

Calculate the displacement of the lens that would be required to focus on an object 25.0 cm from the camera.

State why the lens and the light sensors in a mobile phone camera can be positioned a fixed distance apart.

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.

An object is placed in front of a lens.

Which row of the table shows a combination that will produce a real image of

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.

Which of the following lenses would produce a real image of an object placed 15 cm away from the lens?

Which of the following lenses would produce a real image of an object placed 15 cm away from the lens?

After the light passes through the diffraction grating a line spectrum is observed.

A converging lens can be used to produce a real image on a screen.

A converging lens of focal length 15.0 cm is used to project an image of an illuminated object onto a screen. The object is a circle of diameter 4.0 mm and the image must be as large as possible on a screen of size 0.75 m by 1.25 m.

Calculate the distance between the lens and the screen for this image to be displayed.

A magazine article includes the statement:

If the distance from the lens to the screen is doubled, the brightness of the image is halved.

Assess the validity of this statement.

An object is placed 6.5 cm away from a lens of focal length 3.9 cm. An image is formed 9.8 cm from the lens.

Which of the following is the magnification?

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