Board question: A mirror used for rear-view of an automobile has a focal length 2.0 m. If a car is located at 8.0 m from the mirror – (a) Find out the position of the image of this car as seen in the mirror. (b) Draw the ray-diagram for image formation by the rear-view mirror.
Paper: CBSE 2026 Main 31/4/3 Q37 (3 marks).
What the question asks: find where the image of the car forms, then draw the ray diagram for the mirror.
Key words: a rear-view mirror is a convex mirror. It bulges out towards the road, so it shows a wide view, and its image is always erect (upright) and smaller. Distances are measured from the pole P (the middle of the mirror’s surface) along the principal axis (the line through P and the centre of curvature C).
Step 1, signs (New Cartesian sign convention): distances measured against the direction of the incoming light are negative. The car is in front of the mirror, on the side the light comes from, so u = −8.0 m. A convex mirror’s focus is behind it, so f = +2.0 m.
Step 2, mirror formula: 1/v + 1/u = 1/f (spoken “1 by v plus 1 by u equals 1 by f”). So 1/v = 1/f − 1/u = 1/2 − 1/(−8) = 1/2 + 1/8 = 5/8.
Step 3, flip it: v = 8/5 = +1.6 m. v is positive, so the image is behind the mirror, 1.6 m from the pole.
Step 4, ray diagram (drawn not to scale): a ray parallel to the principal axis reflects as if it came from F behind the mirror; a ray aimed at C (the centre of curvature) hits the mirror head-on and comes straight back. Their dotted extensions behind the mirror meet at the image: small, erect and virtual, between P and F. Draw arrows on the rays to show which way the light goes.
Answer, marking scheme (CBSE 2026 Main 31/4/3 Q37): f = +2 m, u = −8 m; 1/v + 1/u = 1/f (½); 1/v = 1/f − 1/u = 1/2 + 1/8 (½); v = 8/5 = 1.6 m (1): the image is formed 1.6 m behind the mirror; (b) ray diagram (1).
The trap: taking f as −2 m, as for a concave mirror. That puts the image in front of the mirror, which is wrong. A rear-view mirror is convex, so f is plus.
Quick recall (Light): Mirror magnification? → m = −v/u
Comment challenge (CBSE 2024 Main 31/1/1 Q24): An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position of the image formed by the mirror. Answer in the pinned comment.
References: NCERT Class 10 Science, Ch 9 Light – Reflection and Refraction, §9.2 Spherical mirrors (convex mirrors as rear-view mirrors: erect, diminished image, wider field of view; image formation by a convex mirror: virtual, erect, diminished, between P and F; New Cartesian sign convention; mirror formula 1/v + 1/u = 1/f; magnification m = −v/u); CBSE Class 10 board questions and marking schemes.
Narration uses a licensed AI voice (Azure AI Speech, Indian English). Script and physics research by ScoreSpark.
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Board question (CBSE 2026 Main 31/4/3 Q37, 3 marks): A mirror used for rear-view of an automobile has a focal length 2.0 m. If a car is located at 8.0 m from the mirror – (a) Find out the position of the image of this car as seen in the mirror. (b) Draw the ray-diagram for image formation by the rear-view mirror.
Board answer (CBSE marking scheme 2026 Main 31/4/3 Q37): f = +2 m, u = −8 m; 1/v + 1/u = 1/f (½); 1/v = 1/f − 1/u = 1/2 + 1/8 (½); v = 8/5 = 1.6 m (1): the image is formed 1.6 m behind the mirror; (b) ray diagram (1).
Comment challenge (CBSE 2024 Main 31/1/1 Q24): An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position of the image formed by the mirror.
Answer: convex mirror, so f = +15 cm; the object is in front, so u = −10 cm. 1/v = 1/f − 1/u = 1/15 + 1/10 = 5/30 = 1/6, so v = +6 cm: the image is 6 cm behind the mirror (virtual and erect). CBSE 2024 marking scheme (31/1/1 Q24): u = −10 cm, f = +15 cm (½); 1/f = 1/v + 1/u (½); v = +6 cm, image formed behind the mirror (1).
Quick recall (Light): Mirror magnification? → m = −v/u