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?

$0.5={\frac {0.05}{h_{1}}}$

$2={\frac {h_{1}}{0.05}}$

$h_{1}=100{\mbox{ mm}}$