Additional Notes

• Light follows straight lines, or rays, from a source of light to an observer unless it is reflected, by a mirror, or refracted, by a lens, on route.
• Mirrors and lenses come in a variety of shapes to manipulate the light rays in various useful ways. Ray diagrams help us to understand their effects.
• An image is formed at a point where the light rays from an object appear to come from, had their direction not been changed by a mirror or lens. 

• Speed of light: 3 x 10⁸ m/s
• Light ray: Path in which light travels. Can be parallel beam, converging beam or diverging beam.
• Luminous object: Objects which give out light 
• Non-luminous object: those which do not give out light

• Incident ray: Light ray hitting the reflecting surface.
• Reflected ray: Light ray reflected from the reflecting surface.
• Normal: The perpendicular to the reflecting surface at the point of incidence.
• Angle of incidence (i): The angle between the incident ray and the normal. 
• Angle of reflection (r): The angle between the reflected ray and the normal.

• The incident ray, reflected ray and the normal of the reflecting surface lie on the same plane.
  
• Angle of incidence = Angle of Reflection

• Occurs at smooth surfaces.
• Parallel light rays incident on the surface are reflected in one direction only (all rays have the same incident/ reflected ray).
  
• The normals of all points of incidence are equal.

• Occurs at rough surfaces (sandpaper, burnt boots).
  
• Parallel light rays incident on the surface is reflected in all directions.
  
• The normals are not parallel.

• Same size as object
  
• Laterally inverted
  
• Upright
  
• Virtual (not real, cannot be captured on screen)
  
• The distance of the image from the mirror = distance of object from the mirror.

• optical testing
  
• blind corners
• periscopes

• the bending effect of light as it passes through another medium of different density.
• Refraction occurs as the speed of light varies in different media

• The light must pass from one optical medium to another of different optical density
• Angle of incidence more than 0°.

• The incident ray, the normal and the refracted ray all lie on the same plane.
• For 2 particular transparent media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant.
• sin i / sin r = constant
• When light travels from a less dense medium to a denser medium, the ray of light moves towards the normal.
• Likewise, when light travels from a denser to a less dense medium, the ray of light moves away from the normal.
• When light enter a medium perpendicularly, regardless of its density, no deviation of the ray is observed.

• The value of the constant ratio sin i/sin r for a ray passing from air/vacuum to a  give medium is known as the refractive index of the medium.
• The greater the value of the refractive index, the greater the bending of light, the more the light is slowed down and the denser the medium is.

• Red deviates (slows down) the least.
• Violet deviates (slows down) the most.

• Optical Centre (C): The midway point between the lens surface on the principal axis
• Principal axis: The line passing symmetrically through the optical centre of the lens
• Principal focus (F): Point on the principal axis where rays of light converge after passing through the lens
• Focal length (f): Distance between the optical centre, C and the principal focus F.
• Focal plane: Plane which passes through F and P. It is perpendicular to principal axis.

• Principle axis - the principle axis is defined as a line perpendicular to the curved surface of the lens at its center...ie - a line running horizontally through the center of the lens.
• Principle focus - related to the focal length of the lens... ie - one focal length away from the center of the lens (therefore there are two principle foci, one on either side, usually designated F on the far side, and F' on the same side as the object.) Parallel rays of light entering the lens either converge towards the principle focus (convex lenses) or diverge from it (concave lenses).
• Focal length - Focal length is the shortest distance between the principle axis and the principle focus.
• Paraxial rays - Paraxial rays are those that are close to the principle axis and parallel to it.
• Magnification - the magnification is usually defined as image height/object height, representing in effect how much bigger the image is. This is also be directly related to image distance/object distance

Summary: Mirrors, Lenses, Images

MCQ Questions

1. The diagram below shows a plane mirror placed at a distance of 400cm in front of a girl. If the doctor's test card is fixed at 70cm behind the eyes of the girl, what is the distance of the image from the girl?

a. 470m
b. 800m
c. 870m
d. 940m

2. The diagram shows a ray of light moving from air to plastic. Which ratio is the refractive index of plastic?

3. The image seen on the translucent screen of a pinhole camera is
a. real and inverted
b. real and upright
c. virtual and inverted
d. virtual and upright

4. An object is placed in front of a pinhole camera. An image is seen at the centre of the translucent screen when viewed from behind. If the object is now moved slightly nearer and to the observer's right, the image becomes
a. larger and moves to the observer's right
b. larger and moves to the observer's left
c. smaller and moves to the observer's right
d. smaller and moves to the observer's left

5. A light ray does not undergo refraction at a boundary between two media of different optical densities if its angle of incidence is
a. zero
b. 45^o
c. 90^o
d. 180^o

6. An object is placed in front of a lens at a distance less than the focal length of the lens.
The image formed will be
a. real, inverted and diminished
b. real, upright and magnified
c. virtual, inverted and magnified
d. virtual, upright and magnified

7. If the size of the image formed by a converging lens is the same as the object, the object distance is
a. less than the image distance
b. equal to the image distance
c. less than the focal length of the lens
d. equal to the focal length of the lens

8. Which of the following instruments does not contain lenses?
a. microscope
b. camera
c. binoculars
d. periscope

9. A boy walks at a speed of 5m/s towards a plane mirror. The boy and his image in the mirror are moving
a. towards each other at a speed of 5m/s
b. away from each other at a speed of 5m/s
c. towards each other at a speed of 10m/s
d. away from each other at a speed of 10m/s

10. The size of an image formed in a pinhole camera may be increased by
a. placing the object nearer to the camera
b. reducing the size of the object
c. decreasing the distance between the pinhole and the screen
d. making the pinhole bigger

11. In total internal reflection, the angle of incidence is
a. less than the critical angle
b. greater than the critical angle
c. less than the angle of reflection
d. greater than the angle of reflection

12. Total internal reflection can take place in glass and not in air because glass is
a. optically denser than air
b. less transparent than air
c. more transparent than air
d. as optically dense as air

13. The image formed by a slide projector is usually
a. real, inverted and diminished
b. real, inverted and magnified
c. virtual, upright and magnified
d. virtual, inverted and diminished

14. Red light cannot be dispersed by a glass prism because it
a. has a high frequency
b. has a long wavelength
c. does not have component colours
d. is not refracted in glass

15. White light is dispersed using a prism by means of
a. reflection
b. refraction
c. diffraction
d. interference

16. A student uses a converging lens to produce an enlarged virtual image of a scale she wishes to read accurately. The focal length of the lens is 10cm. What is a suitable distance between the scale and the lens?

a. 8cm

b. 10cm

c. 15cm

d. 20cm

17. Which of the following is/are optical device(s) that uses a lens to form a real image of an object?

(1) magnifying glass

(2) pinhole camera

(3) slide projector

a. (3) only

b. (1) and (2) only

c. (1) and (3) only

d. (2) and (3) only

MCQ Answers

1. c
2. c
3. a
4. b
5. a
6. d
7. b
8. d
9. c
10. a
11. b
12. a
13. b
14. c
15. b

16. a

17. a

Structured Questions and Solutions

1. An observer E stands near the edge of a swimming pool. He could see the image of a lamp L1 due to the reflection of light from the surface of the water, which acts like a mirror. L2 and L3 are two other lamps fixed as shown below. 

a. On the diagram, mark the position of the image of L1.

b. Draw two rays to show how E is able to see the image of L1.

c. State whether this image is real or virtual.

d. How would the position of the image of L1 seen by E be affected if the water level in the pool were lowered?

e. Can observer E see the image of L3?

Solution

1a and b.

c. virtual

d. The image will appear further. (because the distance between the lamp and water surface (mirror) is now increased)

e. Yes, the observer can see the image.

2. Figure a and b show light rays reflected to an observer from the surface of each of two mirrors, one plane and the other curved. The normal, N, at each point of incidence has been drawn.

a. Complete both diagrams by drawing accurately the incident rays that would produce the reflected rays shown. The incident rays should start from lines PQ and XY.

b. Write down the lengths of the portion of PQ and XY which observers A and B can see in the two mirrors respectively.

c. Give one reason why the side mirrors of most cars are curved.

Solution

2a.

Note:

• First measure the angle of incidence using a protractor.
• Then draw the reflected ray, with the angle of reflection equal to the angle of reflection.
• Another way is to make use of the images of points X and Y, using the following steps:
• draw a perpendicular line from point X to the mirror, and extend the line upwards to determine the image of point X.
• draw a line linking the image to the normal, and extend it so that the line touches lines PQ and XY.

b. AB: 3.3cm

CD: 5.9cm

c. Provide drivers with a wider field of vision

3. The diagram shows a person whose eyes are 1.6m above the ground. He looks at his reflection in a vertical plane mirror 2.5m away. The top and bottom of the mirror are 2.0m and 1.0m above the ground respectively.

a. How far behind the mirror is the image of the person's head?

b. The person holds the letters 'SET' in front of the mirror. Write down the image of these letters as seen by him. 

c. By drawing light rays, indicate on the diagram which part of his body the person could not see in the mirror.

Solution

4. The diagram below is a scale drawing of a narrow road with a plane mirror mounted across the corner of a 90º bend. The point C represents a car.

a. Mark the position of the car image, formed by reflection at the mirror by a point I.

b. Draw the paths of two rays of light from C by which a man sees this image with his eye positioned as shown in the diagram.

The car travels towards the bend, along the centre line of the road, a distance represented by 10mm on the diagram.

c. Mark I' the position of the image of the car when it has travelled to this position.

d. Draw an arrow on the diagram to show the direction in which the car appears to the man to be travelling.

Solution

5. A plane mirror is inclined at 40º to the floor. An incident ray parallel to the floor strikes the plane mirror as shown.

a. What is the angle of incidence?

b. What is the angle between the incident ray and the reflected ray?

c. The plane mirror is lowered until the inclination is reduced to 20º. What is the change in angle of reflection?

Solution

5a. Angle of incidence is the angle between the normal and the incident ray. 

Angle of incidence = 90º - 40º = 50º

5b. Angle of incidence = angle of reflection

Angle between the incident ray and the reflected ray = 50º + 50º = 100º

5c. Original angle of reflection = 50º

New angle of reflection = 70º

Change in angle of reflection = 70º - 50º = 20º

6. Two men, A and B, are standing in front of a plane mirror as shown.

a. When A looks into the mirror, how far does B seem to be away from him?

b. B starts running towards A at a rate of 1m/s. How fast does B appear to be moving towards A when A looks at the mirror?

c. A starts running towards the mirror at 1m/s. When A looks at the mirror, how fast does his image appear to be moving towards him?

Solution

6a. distance between A and B' = 3 + 3 + 6 = 12m

6b. B will appear to be running towards A at a speed of 1m/s.

6c. A will appear to be running towards himself at a speed of 2m/s.

7. An artist leans his back against a painted wall while looking into a 1m long mirror at the opposite end of a rectangular room.

a. How many metres of the painted wall can he see in the 1m long mirror?

b. The artist moves forward such that he is 5m from the mirror. How many metres of the painted wall can he see in the 1m long mirror?

Solution

7a. Assume that the artist is facing the centre of the mirror. To see the maximum range, he has to look at the two extreme ends of the mirror. By applying angle of incidence = angle of reflection, the maximum length of the painted wall is 2m.

7b. Assume that the artist is facing the centre of the mirror. To see the maximum range, he has to look at the two extreme ends of the mirror. Applying the principle angle of incidence = angle of reflection,

DC = 0.5m

BD = 0.5m (ABC is an isoceles triangle)

Triangle ADB is similar to triangle AFE

AD/BD = AF/EF 

5/0.5 = 15/EF

EF = 1.5m

GH = EF = 1.5m

The maximum length of the painted wall is 1.5m + 1m + 1.5m = 4m

8. A ray of light travels from air into a semicircular prism and emerges into the air again as shown below. The refractive index of air is 1.0.

a. What is the critical angle of the prism material?

b. What is the refractive index of the prism material?

c. The light ray is rotated anti-clockwise causing such that angle a is changed to 50º. Draw on the diagram the new positions of the incident ray and refracted ray.

d. The light ray is rotated clockwise such that angle a is changed to 70º. Draw the new positions of the incident ray and refracted ray.

Solution

8a.critical angle = 90º - 60º = 30º

8b. sin c = 1/n

sin 30 = 1/n

n = 2.0

8c.

8d. n_i sin i = n_r sin r

2 x sin 20 = 1 x sin r

r = 43.2º

9. An object O is placed in front of a thin converging lens of focal point F as shown below.

a. Complete the ray diagram to locate the position of the image formed by the converging lens.

bi. What are the characteristics of the image formed?

bii. Name an application for such an arrangement.

ci. What happens to the size and position of the image when the object is moved slightly to the left?

cii. Name an application for such as arrangement.

di. What happens to the size and position of the image when the object is moved slightly to the right?

dii. Name an application for such an arrangement.

Solution

9a.

9bi. real, inverted and same size as object

9bii. photocopier

ci. The image gets smaller and image distance from the lens decreases.

cii. camera

di. The image gets bigger and image distance from the lens increases.

dii. projector

10. An object O is placed in front of a thin converging lens of focal point F as shown below.

a. In the diagram above, draw rays to locate the position of the image formed by the converging lens.

b. What are the characteristics of the image formed?

c. What happens to the size and position of the image when the object is moved nearer to the left, towards the focal point?

Solution

15a.

15b. virtual, upright, magnified

15c.The image gets bigger and image distance from the lens increases.

16. An object O is placed in front of a thin diverging lens of focal point F as shown below.

a. In the diagram above, draw rays to locate the position of the image formed by the diverging lens.

b. What are the characteristics of the image formed by a diverging lens?

c. What happens to the size and position of the image when the object is moved nearer to the diverging lens?

Solution

16a.

16b. virtual, upright, diminished

16c.The image gets bigger and image distance from the lens decreases.