Light travels in straight lines and changes direction when it meets a surface. This chapter covers the laws of reflection, image formation by plane and spherical mirrors, the mirror formula, refraction through glass slabs and lenses, the lens formula, magnification and the power of a lens.
An object is placed 30 cm in front of a concave mirror of focal length 15 cm. Find the position and nature of the image.
Using the sign convention: u = −30 cm and f = −15 cm.
Mirror formula: 1/v + 1/u = 1/f
1/v = 1/f − 1/u = (−1/15) − (−1/30)
= −1/15 + 1/30 = (−2 + 1)/30 = −1/30
So v = −30 cm.
The negative sign shows the image forms 30 cm in front of the mirror (on the same side as the object), so it is real and inverted.
Magnification: m = −v/u = −(−30)/(−30) = −1, so the image is the same size as the object.
Note that the object is at the centre of curvature (R = 2f = 30 cm), which is exactly the position that gives a same-size real image.
Formula: 1/v + 1/u = 1/f; m = −v/u; f = R/2
Final Answer: The image forms 30 cm in front of the mirror; it is real, inverted and the same size as the object.
Common Mistake: Forgetting that u and f are negative for a concave mirror under the sign convention.
Exam Tip: Write the sign convention values before substituting — most mistakes here are sign mistakes.
Q2. Question 2 — Power of a Lens
Find the power of a concave lens whose focal length is 25 cm.
For a concave (diverging) lens the focal length is taken as negative.
f = −25 cm = −0.25 m
Power of a lens: P = 1/f, with f measured in metres.
P = 1/(−0.25) = −4 D
The negative sign shows that the lens is diverging.
Formula: P = 1/f (f in metres); unit = dioptre (D)
Final Answer: P = −4 D (the minus sign indicates a concave, diverging lens).
Common Mistake: Substituting the focal length in centimetres, which gives an answer 100 times too large.
Exam Tip: Convert cm to m first, and never drop the sign — it tells the examiner the type of lens.
Q3. Question 3 — Convex Mirror as Rear-view Mirror
Why is a convex mirror preferred over a plane mirror as a rear-view mirror in vehicles?
A convex mirror always forms an image that is virtual, erect and smaller than the object, no matter where the object is placed.
Because the image is diminished, a large area behind the vehicle fits into a small mirror, which means a convex mirror gives a much wider field of view than a plane mirror of the same size.
The image also stays erect, so the driver sees the traffic the right way up.
Together these two properties let the driver see more of the road behind, which is why convex mirrors are used.
Final Answer: Because it always gives an erect, diminished virtual image and therefore a much wider field of view than a plane mirror.
Common Mistake: Saying a convex mirror magnifies the image — it always diminishes it.
Exam Tip: Mention both points: wider field of view AND erect virtual image.
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