A-level Physics (Advancing Physics)/Lenses/Worked Solutions

1. A lens has a focal length of 10 cm. What is its power, in dioptres?

Always use SI units, so 10 cm = 0.1m.

$$P = \frac{1}{f} = \frac{1}{0.1} = 10\mbox{ D}$$

'''2. Light reflected off a cactus 1.5m from a 20D lens forms an image. How many metres is it from the other side of the lens?'''

u must be negative, as per the Cartesian convention, so u = -1.5.

$$\frac{1}{v} = \frac{1}{-1.5} + 20 = \frac{58}{3}\mbox{ D}$$

$$v = \frac{3}{58} = 0.0517\mbox{ m} = 51.7\mbox{ mm}$$

'''3. A lens in an RGB projector causes an image to focus on a large screen. What sort of lens is it? Is its power positive or negative?'''

The wavefronts are being caused to spread out (diverge) more by the lens. Hence, it is a diverging lens. The wavefronts are losing curvature, so the lens has a negative power.

4. What is the focal length of a 100D lens?

$$100 = \frac{1}{f}$$

$$f = \frac{1}{100} = 0.01\mbox{ m} = 10\mbox{ mm}$$

'''5. The film in a camera is 5mm from a lens when automatically focussed on someone's face, 10m from the camera. What is the power of the lens?'''

5mm = 0.005m

$$\frac{1}{0.005} = \frac{1}{-10}+ P$$

$$200 = P - 0.1$$

$$P = 200.1\mbox{ D}$$

Since lenses are generally made to have nice round powers, this was probably a 200D lens. However, this is in real life, and this an hypothetical question with numbers picked out of thin air by me.

'''6. The light from a candle is enlarged by a factor of 0.5 by a lens, and produces an image of a candle, 0.05m high, on a wall. What is the height of the candle?'''

$$0.5 = \frac{0.05}{h_1}$$

$$2 = \frac{h_1}{0.05}$$

$$h_1 = 100\mbox{ mm}$$