Ray Optics: Diagram-Based Questions (3)

hard • 3 min read
Tags Ray Optics

Question

An object is placed 3030 cm in front of a concave mirror of focal length 1010 cm. Find the position, size, and nature of the image. The object height is 22 cm.

The diagram shows a concave mirror with the object on the principal axis, the principal focus marked, and the centre of curvature beyond it. We use the standard sign convention: distances measured against the direction of incident light are negative.

Solution — Step by Step

For a concave mirror, focal length ff is negative (mirror is on the left, focal point is to the left of the pole).

f=−10f = -10 cm, u=−30u = -30 cm (object on the left).

1v+1u=1f\frac{1}{v} + \frac{1}{u} = \frac{1}{f}

1v=1f−1u=1−10−1−30=−110+130=−330+130=−230\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{-10} - \frac{1}{-30} = -\frac{1}{10} + \frac{1}{30} = -\frac{3}{30} + \frac{1}{30} = -\frac{2}{30}

v=−15 cmv = -15 \text{ cm}

m=−vu=−−15−30=−12m = -\frac{v}{u} = -\frac{-15}{-30} = -\frac{1}{2}

Image height =m×= m \times object height =−12×2=−1= -\tfrac{1}{2} \times 2 = -1 cm.

v=−15v = -15 cm: image is on the same side as the object (real, since concave mirror images on the same side are real).

m=−1/2m = -1/2: image is inverted (negative sign) and diminished (magnitude < 1).

Final answer: Image is real, inverted, diminished, located 1515 cm in front of the mirror, with height 11 cm.

Why This Works

The sign convention is the entire game in ray optics. Once you commit to “incident light goes left to right, distances measured left of pole are negative,” every formula becomes mechanical.

For a concave mirror, when the object is beyond C (centre of curvature), the image is real, inverted, diminished, between F and C. We placed the object at 3030 cm with C=2f=20C = 2f = 20 cm, so the object is beyond C, and the result matches.

Mirror: 1v+1u=1f\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}, m=−vum = -\dfrac{v}{u}

Lens: 1v−1u=1f\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}, m=vum = \dfrac{v}{u}

For concave mirror and concave lens, f<0f < 0. For convex mirror and convex lens, f>0f > 0. (Some textbooks flip mirror conventions — stick with one.)

Alternative Method

Ray diagram. Draw two rays from the object tip: one parallel to the axis (reflects through F), one through C (returns along itself). Their intersection on the same side is the image. You can read off v≈−15v \approx -15 cm and verify the image is inverted and half the size.

For NEET diagram MCQs, draw a quick ray diagram — even a rough one — before applying the formula. Visual + algebraic agreement catches sign errors fast.

Common Mistake

Students plug in f=+10f = +10 for the concave mirror, get v=+6v = +6 cm, and conclude the image is virtual. The first sign of trouble: a real image should be on the same side as the object for a concave mirror — if your vv has the “wrong” sign, recheck ff. Concave is negative, convex is positive (for both mirrors and lenses, in the Cartesian convention used in NCERT).

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