HCI Worksheet 3 Lenses and Refraction (answers)

Hwa Chong Institution Sec 3 (Physics) 1 Name: _____________________________________ Class: ________ Date: ___________ Sec 3 Physics Worksheet 3: Reflection, refraction and lenses (answers) Reflection 1 The diagram, drawn to scale, shows a very small bright light at S shining into a darkened room through a window set in a vertical wall. A scale is marked in metres on the floor as shown. a (i) Draw two rays to show the limits of the bright patch on the scale, and measure the length of the scale that is illustrated. [1] Length of bright patch = 6 m [1] (ii) Which property of light rays does this example demonstrate? Light rays travel in straight line. [1] b The window is now covered with a plane mirror as shown below. (i) Show how two rays from S are reflected by the mirror and use them to locate the image of S. Mark clearly the position of the image of S. [2]

Hwa Chong Institution Sec 3 (Physics) 2 (ii) Write down one characteristic of this image. Image is virtual / laterally inverted / same size as the object / upright. [1] 2 The diagram shows two mirrors X and Y, and a solid object with a coloured spot at O, the centre of its left hand face. a An eye at A sees an image of O resulting from the reflection at the mirror X. Mark I, the position of this image, and draw a ray from O to the eye at A. [1] b When the eye is moved to B, it sees an image of O resulting from reflections at both mirrors. Draw a ray of light from O which enables the eye at B to see this image. [2]

Hwa Chong Institution Sec 3 (Physics) 3 Refraction 3 a With the aid of a suitable diagram define the term refractive index as applied to an optical material. definition consistent with diagram n = ; with i in air or vacuum; [2] The diagram below shows the path followed by a ray of red light that is incident on one face of a glass prism at an angle θ to the normal. Marking points: refraction at first surface; refraction at emergent surface; deviation greater than red light; If the refractions are correct but the angle of refraction is less than that for red light award [2]. b (i) The red light is now replaced by blue light. On the diagram sketch the corresponding path followed by a ray of blue light incident at the same angle θ. [3] Air or vacuum Materialr i r i sin sin Incident beam normal red blue

Hwa Chong Institution Sec 3 (Physics) 4 (ii) State and explain whether the refractive index for red light in the glass is greater than, equal to or less than the refractive index for blue light. less — refraction angle is greater therefore sin i / sin r is smaller; [1] 4 This question is about optical dispersion. The graph below shows the variation with wavelength λ of the speed v of light in one type of glass. a Use data from the graph to determine, to the correct number of significant digits, the refractive index for blue light of wavelength 400 nm in this type of glass. (free space speed of light c = 2.9979 × 108 m s–1) for blue, from the graph v =1.9455 (±0.0005) × 108 m s–1; ( ).  . . . 2 9979 1 5409 0 00051 9455 cn v= = =  [2] b The refractive index of red light of wavelength 650 nm in this type of glass is about 1.52. Use this fact and your answer in (a) to explain optical dispersion. white light contains light of different wavelengths; each wavelength is deviated by a different amount as it passes through the prism / the refractive index of the prism is dependent on the wavelength / OWTTE; the refractive index is larger for blue light, therefore the refractive angle is smaller; and so blue light is bent more towards the normal / OWTTE; Alternatively, the response may use the aid of a diagram. [2] 1.9700 1.9650 1.9600 1.9550 1.9500 1.9450 1.9400 1.9350 v /×10 m s –18 350 400 450 500 550 600 650 700 750 / nm

Hwa Chong Institution Sec 3 (Physics) 5 5 This question is about refractive index and critical angle. The diagram below shows the boundary between glass and air. a On the diagram, draw a ray of light to illustrate what is meant by critical angle. Mark the critical angle with the letter “c”. [3] Marking points: light incident from glass; emergent ray along boundary; c marked correctly; A straight optic fibre has length 1.2 km and diameter 1.0 mm. Light is reflected along the fibre as shown below. At each reflection, the angle of incidence is equal in value to the critical angle. The refractive index of the glass of the fibre is 1.5. b Deduce that the length of the light path along the optic fibre is about 1.8 km. sin . 1 15c= ; for every 1.0 mm length, light travels 1.5 mm; path length = 1.2 km × 1.5 = 1.8 km; Award [4] for any correct calculation that leads to 1.8 km. glass air 1.2 km 1.0 km 1.0 mm c

Hwa Chong Institution Sec 3 (Physics) 6 The speed of light in the fibre is 2.0 × 108 m s–1. c Calculate the time for a pulse of light to travel the length of the fibre when its path is (i) along the axis of the fibre. time = = 6.0 s; [1] (ii) as calculated in (b). time = 9.0 s; [1] 6 This question is about refractive index. Light from a laser is directed at a semi -circular glass block. The light passes undeviated through the block and on to a screen, forming a spot at A as shown. The semi-circular block is rotated about the point P. The spot of light on the screen is seen to move downwards. When the spot reaches point B, it disappears. a Complete the diagram below to show the position of the semi-circular block when the spot is at point B. The original position of the block is shown as a dotted line. Marking point: diagram showing ray emerging along flat face; [1] 8100.2 1200  Laser P A B Laser P A B

Hwa Chong Institution Sec 3 (Physics) 7 In a particular experiment, the distance PA is 120 cm and distance AB is 138 cm. b Calculate the refractive index of the glass of the block. tan 138 120 = , θ = 49.0°; critical angle = 41.0°; .sin 1 1 52n c== ; (allow ecf if sensible) 3 Award [1 max] if the critical angle is = 49.0° or (answer .sin 1 1 33n c== ). [3] The laser is changed for one emitting light of higher frequency. The experiment is then repeated. c State and explain whether the distance AB will be greater or less than 138 cm. n is greater at higher frequency so C is smaller; hence AB is larger; [3] 7 A bird is hovering above a pond. A fish is in the pond at the position shown in the diagram below. a Draw rays on the diagram above to locate the position of the image of the fish as seen by the bird. [3] b Explain whether the image of the fish is real or virtual. virtual since extension of rays gives its position / appear to come from fish / OWTTE; [1] one ray from fish with correct refraction; 2nd ray from fish with correct refraction; rays backward to give correct position of image; Here only a qualitative explanation (diagram) is expected, since no numerical values are given. A quantitative solution is asked for in part (a)(iii).

Hwa Chong Institution Sec 3 (Physics) 8 c The fish is 48 cm below the surface of the pond. The bird hovers vertically above the fish. Calculate the apparent depth of the fish. The refractive index of water is 1.3. ;real depth apparent depthn= . 48apparent depth 37 cm13== ; [2] 8 This question is about dispersion and refractive index. a State and explain what is meant b