JEE Main: Find Focal Length When Magnification = 1/4 | Mirror Formula Trick 💡
❓ Question A mirror produces an image with a magnification of 1/4 . If the distance between the object and its image is 40 cm , find the focal length of the mirror. 🖼️ Question Image ✍️ Short Solution Step 1 — Recall the mirror and magnification formulas For any spherical mirror: 1 f = 1 u + 1 v and m = h i h o = − v u Given: m = 1 4 ⇒ v = − u 4 ( Negative sign shows image is virtual and erect → convex mirror case. ) Step 2 — Use the separation between object and image Distance between object and image is given as 40 cm: ∣ v − u ∣ = 40 Since v = − u 4 v = -\frac{u}{4} : ∣ − u 4 − u ∣ = 40 | -\frac{u}{4} - u | = 40 ∣ − 5 u 4 ∣ = 40 | -\frac{5u}{4} | = 40 5 ∣ u ∣ 4 = 40 ⇒ ∣ u ∣ = 32 cm \frac{5|u|}{4} = 40 \Rightarrow |u| = 32 \text{ cm} So, u = − 32 cm u = -32 \text{ cm} (object in front of mirror). Then, v = − u 4 = − ( − 32 ) / 4 = + 8 cm v = -\frac{u}{4} = -(-32)/4 = +8 \text{ cm} ( Positive v → virtual image behind mirror → c...