MHT-CET Physics · Optics (Ray)

Mirrors

A spherical mirror of focal length f = R/2 forms an image where 1/v + 1/u = 1/f, with magnification −v/u; a plane mirror gives an erect image of the same size, and two plane mirrors at an angle θ give 360°/θ − 1 images.

All Optics (Ray) notes MHT-CET Physics strategy

Why this matters

5 PYQs, one HARD: the object distance for a real image n times larger, the speed of an object read from its image's motion in a convex mirror, the number of images between two mirrors, a plane mirror's magnification, and a half-covered mirror. One card.

Concept 1 of 1: The Mirror Formula and Plane Mirrors

With the Cartesian sign convention the mirror formula is 1/v + 1/u = 1/f and the magnification is −v/u. A real image n times the size of the object means v = nu (both in front), so u = (n + 1)f/n. For a convex mirror, the formula turns an image position into an object position, so a moving image gives the object's speed. A plane mirror has magnification +1. Two plane mirrors at θ form 360°/θ − 1 images: three images at 90°. Covering half a mirror leaves every point of the image formed by the rest of the mirror, so the image is complete but dimmer.

Definition

$\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$ , $f = \dfrac{R}{2}$ , $m = -\dfrac{v}{u}$ .
Real image n times larger: $u = \dfrac{(n + 1)f}{n}$ .
Plane mirror: m = +1. Two mirrors at θ: $\dfrac{360^\circ}{\theta} - 1$ images (90° ⇒ 3).
Half the mirror covered: full image, lower intensity.

Mirror formula

\frac{1}{v} + \frac{1}{u} = \frac{1}{f}, \qquad m = -\frac{v}{u}

Worked example

An object is 30 cm in front of a concave mirror of focal length 20 cm. Image position and magnification?

Practice this conceptself-check · 1 quick reps

The same idea in a real exam question:

MHT-CET · 2023 · 2nd May Shift 2 · Q20Moderate

Example 1 · Optics (Ray) · Mirrors and Image Formation

A concave mirror of focal length 'f' produces an image 'n' times the size of the object. If the image is real, then the distance of the object from the mirror is

Thinking a half-covered mirror forms half an image

Every part of the mirror receives light from every point of the object. Covering half removes half the light, not half the picture.

Drill 4 more on the mirror formula and plane mirrors

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

The Mirror Formula and Plane Mirrors
Mirror formula
$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}, \qquad m = -\frac{v}{u}$

Watch out for (1)

Thinking a half-covered mirror forms half an image
→ The Mirror Formula and Plane Mirrors

Test yourself on Optics (Ray)

20 past MHT-CET questions from this chapter, timed at 18 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

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