Spherical Surfaces and Thin Lenses — Part 2: Magnification, power and combinations: visual lesson, ISC Class 12 Physics

Lesson

Magnification, Power and Lens Combinations

Part 2 — how large the image is, how strong a lens is, and what happens when lenses and mirrors work together.

In this lesson you will

Use the thin lens formula with m = v/u and P = 1/f, with correct signs
Derive 1/F = 1/f₁ + 1/f₂ and P = P₁ + P₂ for thin lenses in contact
Locate the final image formed by separated lenses and by a lens with a mirror

Diagram

Images formed by a convex lens

Table of images formed by a convex lens for five object positions, from infinity to inside the focus
Object (convex lens)	Image	Nature
At infinity	At F₂	Real, inverted, point-sized
Beyond 2F₁	Between F₂ and 2F₂	Real, inverted, smaller
At 2F₁	At 2F₂	Real, inverted, same size
Between F₁ and 2F₁	Beyond 2F₂	Real, inverted, larger
Between F₁ and O	Same side as the object	Virtual, erect, larger

Use $\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$ with $f > 0$ . Three easy rays fix the image: parallel to the axis → through $F_2$ ; through O → undeviated; through $F_1$ → parallel.

Real images form on the far side ( $v > 0$ ) whenever the object is beyond $F_1$ .

Concept

Magnification of a lens

The ray through the optical centre is undeviated, so the triangles ABO and A′B′O are similar: $m = \dfrac{h'}{h} = \dfrac{v}{u}$ (For a mirror $m = -v/u$ ; for a lens the minus sign is absent because the image forms on the far side.)

m negative: real and inverted; m positive: virtual and erect.

Table of what the sign and size of the magnification of a lens mean, and the magnification of a single refracting surface
Lens result	Meaning
$m = v/u$ negative	Real, inverted image (opposite side)
$m$ positive	Virtual, erect image (same side as the object)
$\|m\| > 1$ / $\|m\| < 1$	Enlarged / diminished
Single surface	$m = \dfrac{n_1 v}{n_2 u}$

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