Reflection and Mirrors: Quick Revision

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

The big ideas

• The angle of incidence equals the angle of reflection, both measured from the normal.
• A plane mirror gives a virtual, upright image of the same size, as far behind the mirror as the object is in front, with left and right swapped.
• For a spherical mirror, $f = \dfrac{R}{2}$: the focus is half way between the pole and the centre of curvature.
• A concave mirror gives real images (object beyond $F$) or a larger virtual image (object inside $F$).
• A convex mirror always gives a smaller, virtual, upright image between $P$ and $F$.
• Mirror formula $\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$, and $m = \dfrac{h'}{h} = -\dfrac{v}{u}$.

The facts at a glance

A worked example

An object $3\ \text{cm}$ tall stands $40\ \text{cm}$ from a concave mirror of focal length $16\ \text{cm}$. Find the image.

1. The signs. $u = -40\ \text{cm}$, $f = -16\ \text{cm}$.
2. The image. $\dfrac{1}{v} = -\dfrac{1}{16\ \text{cm}} + \dfrac{1}{40\ \text{cm}} = \dfrac{-5 + 2}{80\ \text{cm}} = -\dfrac{3}{80\ \text{cm}}$, so $v = -26.7\ \text{cm}$.
3. The size. $m = -\dfrac{v}{u} = -0.667$, so $h' = -0.667 \times 3\ \text{cm} = -2\ \text{cm}$.

The image is $26.7\ \text{cm}$ in front of the mirror: real, inverted and $2\ \text{cm}$ tall. The object is beyond $C$ ($32\ \text{cm}$), as the table says.

Practice with new numbers

A program to try

The program uses the mirror formula for any mirror, and says what the image is like.

Mistakes to avoid

• Measuring angles from the mirror surface. The laws use the normal.
• Giving a concave mirror a positive $f$. In this convention it is negative.
• Dropping the minus sign in $m = -\dfrac{v}{u}$. It is part of the mirror's formula.
• 'A concave mirror always gives a real image.' Not inside $F$.

Check yourself

1. A ray makes $35^\circ$ with the surface of a plane mirror. What is the angle of reflection?

2. A concave mirror has $R = 46\ \text{cm}$. Where should a bulb go for a parallel beam?

3. Which mirror can only give virtual images?

4. A concave mirror gives $m = +2.5$. What is the image like, and where is the object?