Lenses and Their Power: Quick Revision

A brief note on Lenses and Their Power. Read it before a test. Try each question at the end before you open its answer.

The big ideas

• A convex lens is thick in the middle and brings parallel rays together at $F_2$. A concave lens is thin in the middle and spreads them, as if from $F_1$.
• Ray rules: parallel to the axis, then through $F_2$; through $O$, straight on; through $F_1$, then parallel.
• A convex lens gives real, inverted images (object beyond $F_1$) or a larger virtual image (object inside $F_1$). A concave lens always gives a smaller, virtual, upright image.
• Lens formula $\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$, and $m = \dfrac{v}{u}$.
• Power $P = \dfrac{1}{f}$ with $f$ in metres, in dioptres. Lenses in contact: the powers add.

The facts at a glance

A worked example

A slide is $35\ \text{cm}$ from a convex lens of focal length $20\ \text{cm}$. Where must the screen be, how large is the picture, and what is the power of the lens?

1. The image. $\dfrac{1}{v} = \dfrac{1}{20\ \text{cm}} - \dfrac{1}{35\ \text{cm}} = \dfrac{7 - 4}{140\ \text{cm}} = \dfrac{3}{140\ \text{cm}}$, so $v = +46.7\ \text{cm}$.
2. The size. $m = \dfrac{46.7\ \text{cm}}{-35\ \text{cm}} = -1.33$: inverted and $1.33$ times larger.
3. The power. $P = \dfrac{1}{0.20\ \text{m}} = +5\ \text{D}$.

The slide is between $F_1$ and $2F_1$, so the picture is real, inverted and larger: a projector.

Practice with new numbers

A program to try

The program finds the image of a convex lens and the power of the lens.

Mistakes to avoid

• Using the mirror formula for a lens. For a lens it is $\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$.
• Putting $f$ in centimetres into $P = \dfrac{1}{f}$. Use metres.
• Drawing a lens's real image on the object's side. It forms on the far side.
• Forgetting that a concave lens has a negative $f$ and $P$.

Check yourself

1. Which kind of lens can form a real image?

2. A spectacle lens has a power of $-5\ \text{D}$. What kind of lens is it, and what is its focal length?

3. An object stands at $2F_1$ of a convex lens of focal length $13\ \text{cm}$. Where is the image?

4. Lenses of $+3\ \text{D}$ and $+1.5\ \text{D}$ are in contact. What is the focal length of the pair?