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Lesson: Chapter 5 — Optics

Putting the chapter together 2 of 3

The exercise

Worked answers to exercises 5.1 and 5.2 from the textbook.

Exercise 5.1 — the angler and the fish

A man fishing with a rod sees a fish in the water

  1. Why does the fish look a little higher than it is?
  2. Show with a ray diagram how it appears raised.

The answer

  1. Light from the fish bends away from the normal as it leaves the water (denser to rarer), so traced back it seems to come from a point above the fish.
  2. The diagram is the same as for the coin at the bottom of the water.
Rays from an object under water bending away from the normal at the surface; traced back they meet above the object.

Exercise 5.2, question 1 — mirrors

Mirrors and their images

  1. Name two kinds of mirror that always form a virtual image of an object in front of them.
  2. An object is between the focus and a concave mirror. Is the image upright or inverted, larger or smaller, real or virtual? As the object moves from the focus towards the pole, does the image grow or shrink?
  3. Where must the object be for a concave mirror to form its largest real image? Is it upright or inverted?
  4. Give two properties shared by every image in a convex mirror.

The answer

  1. Plane mirrors and convex mirrors.
  2. Upright, larger, virtual. It grows smaller as the object moves towards the pole.
  3. Just beyond the focus, between F and C. It is inverted.
  4. Any two of: smaller than the object, upright, virtual.

Question 3 — total internal reflection

Rays going from water into air at different angles

  1. What is total internal reflection?
  2. Give an example where it happens.

The answer

  1. When light going from a denser into a rarer medium meets the boundary at more than the critical angle, it is reflected entirely back into the denser medium.
  2. Light travelling along an optical fibre; a 45° prism in binoculars.
Light in water striking the surface beyond the critical angle and being totally internally reflected.

Question 6 — three unlabelled lenses

A bag holds three convex lenses of focal length 10 cm, 20 cm and 25 cm, not labelled. How can you tell them apart?

Describe a simple activity.

The answer

Use each lens to form a sharp image of a distant window or tree on a screen (Activity 5.6) and measure the lens-to-screen distance. That distance is roughly the focal length: about 10 cm, 20 cm or 25 cm tells you which lens is which.

Question 13 — an image drawn to scale

A convex lens has focal length 30 mm. An object 20 mm tall stands 15 mm from it. Find the image by a scale drawing, give two of its properties, and how many times taller it is than the object.

The object is inside the focal length.

The answer

To scale: an object 20 mm tall, 15 mm from a convex lens of focal length 30 mm; the rays, traced back, meet 30 mm from the lens on the object's side at an upright image 40 mm tall.

The image is 30 mm from the lens, on the same side as the object.

It is upright and virtual.

height of image ÷ height of object = 40 mm ÷ 20 mm

= 2 times