Light – Reflection and Refraction • Topic 1 of 3

Reflection & Spherical Mirrors

When light falls on a polished surface it bounces back into the same medium — this turning back of light is called reflection. The ray that strikes the surface is the incident ray, the one that bounces off is the reflected ray, and the line drawn perpendicular to the surface at the point of incidence is the normal. Two laws govern every reflection, whether from a plane mirror or a curved one.

The laws of reflection are:

The angle of incidence ($\angle i$) is always equal to the angle of reflection ($\angle r$), i.e. $\angle i = \angle r$.
The incident ray, the reflected ray and the normal at the point of incidence all lie in the same plane.

A plane mirror gives an image that is virtual, erect, the same size as the object and laterally inverted, formed as far behind the mirror as the object is in front. Curved mirrors are far more useful. A spherical mirror is a small part of a hollow sphere whose one surface is silvered. If the reflecting surface is the inner (caved-in) side it is a concave mirror; if it is the bulged-out side it is a convex mirror.

Key terms for a spherical mirror are worth memorising. The pole (P) is the centre of the mirror's reflecting surface. The centre of curvature (C) is the centre of the sphere of which the mirror is a part, and the radius of curvature (R) is the distance PC. The principal axis is the straight line passing through P and C. The principal focus (F) is the point on the principal axis where rays parallel to the axis meet (concave) or appear to diverge from (convex) after reflection. The distance PF is the focal length (f), and for a spherical mirror $f = \frac{R}{2}$.

Two simple ray rules let you draw any image. A ray parallel to the principal axis passes through F (or appears to come from F) after reflection; a ray through C (or directed towards C) returns along the same path because it strikes the mirror normally. In a concave mirror, the nature, position and size of the image change as the object moves from infinity towards the pole — it can be real and inverted, or virtual and enlarged when the object is between P and F. A convex mirror always gives a virtual, erect, diminished image, which is why it is used as a rear-view mirror and at blind corners. Concave mirrors are used in torches, shaving mirrors, headlights and solar furnaces.

Solved Examples

Worked Example

A ray of light strikes a plane mirror at an angle of incidence of $35^\circ$. What is the angle of reflection, and what is the angle between the incident and reflected rays?

Solution

By the first law of reflection, $\angle r = \angle i = 35^\circ$.
The angle between the incident ray and the reflected ray $= \angle i + \angle r = 35^\circ + 35^\circ$.
$= 70^\circ$.

Answer: Angle of reflection $= 35^\circ$; angle between the rays $= 70^\circ$.

Worked Example

The radius of curvature of a concave mirror is $30\,\text{cm}$. Find its focal length.

Solution

For a spherical mirror, $f = \frac{R}{2}$.
$f = \frac{30}{2} = 15\,\text{cm}$.

Answer: Focal length $= 15\,\text{cm}$.

Worked Example

A spherical mirror has a focal length of $20\,\text{cm}$. What is its radius of curvature?

Solution

Since $f = \frac{R}{2}$, we have $R = 2f$.
$R = 2 \times 20 = 40\,\text{cm}$.

Answer: Radius of curvature $= 40\,\text{cm}$.

Worked Example

An object is placed beyond the centre of curvature of a concave mirror. Describe the nature, position and size of the image.

Solution

When the object is beyond C, the two standard rays (parallel ray through F, and ray through C) meet between F and C.
The image is therefore formed between F and C.
It is real (rays actually meet), inverted, and diminished (smaller than the object).

Answer: Real, inverted and diminished, formed between F and C.

Worked Example

Why is a convex mirror preferred as a rear-view mirror in vehicles?

Solution

A convex mirror always forms a virtual, erect and diminished image, whatever the position of the object.
Because the image is diminished, the mirror covers a much wider field of view than a plane mirror of the same size.
The driver can therefore see a larger area of traffic behind the vehicle in a small mirror.

Answer: It gives an erect, diminished image and a wide field of view, so more traffic is visible behind the vehicle.

Worked Example

An object is placed between the pole and the focus of a concave mirror. State the nature and size of the image formed.

Solution

When the object lies between P and F, the reflected rays diverge and do not meet in front of the mirror.
On extending them backwards they appear to meet behind the mirror.
So the image is virtual and erect, and it is larger than the object (magnified).

Answer: Virtual, erect and magnified, formed behind the mirror.

Key Points

Laws of reflection: angle of incidence equals angle of reflection ($\angle i = \angle r$), and incident ray, reflected ray and normal lie in one plane.
A concave mirror reflects from the caved-in surface; a convex mirror reflects from the bulged-out surface.
Key terms: pole (P), centre of curvature (C), radius of curvature (R), principal axis, principal focus (F) and focal length (f).
For a spherical mirror, $f = \frac{R}{2}$.
A convex mirror always gives a virtual, erect, diminished image; a concave mirror's image depends on object position.

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.The laws of reflection hold for:

Explanation: The laws of reflection apply to every reflecting surface, plane or curved.

Q2.The relation between focal length and radius of curvature of a spherical mirror is:

Explanation: For a spherical mirror the focal length is half the radius of curvature, $f = \frac{R}{2}$.

Q3.Which mirror always forms a virtual, erect and diminished image?

Explanation: A convex mirror gives a virtual, erect, diminished image for every object position.

Q4.An object placed between the pole and focus of a concave mirror forms an image that is:

Explanation: When the object is between P and F, a concave mirror forms a virtual, erect and magnified image behind the mirror.

Practice more MCQs → 📝 Assignment · 30 marks