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.

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

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.

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

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

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?

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

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

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

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

$200=P-0.1$

$P=200.1\text{ D}$

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?

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

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

$h_1=100\text{ mm}$