SPI Physics · Light and Optics

Refraction and Lenses

Light bends when it passes from one medium into another because its speed changes; the refractive index n = c/v measures how much it slows, and a lens uses this bending to form images.

All Light and Optics notes

Why this matters

Four questions in the bank, all MODERATE: which pair of media changes light the most, how the pins are lined up in the glass slab experiment, what water does to a lens's power, and the point where a convex lens gives u = v. Each needs a reason, not a recalled word, so learn why light bends as well as which way.

Concept 1 of 2: Refractive index and the bending of light

Light slows down in glass or water. When it enters at a slant, one side of the beam slows first, so the beam swings round, like a car whose left wheels hit sand before its right wheels. The more the speed changes, the more it bends.

Definition

Refractive index $n = \dfrac{c}{v}$ : the speed of light in a vacuum over its speed in the medium. A higher n means slower light.
Going into a medium of higher n (optically denser), light bends towards the normal; going into a lower n, away from it.
The bending is greatest where the two refractive indices differ the most.
Through a glass slab the ray comes out parallel to the ray that went in, only shifted sideways.
In the pin experiment the pins may lean, so you line up their feet (where they enter the paper), not their heads.
A glass lens (n about 1.5) bends light because it differs from the air (n = 1). In water (n about 1.33) the difference is smaller, so the lens bends light less and its focal length becomes longer.

Refractive index

n = \frac{c}{v} \qquad n_{21} = \frac{n_2}{n_1} = \frac{v_1}{v_2}

cspeed of light in a vacuum, 3 × 10⁸ m/s
vspeed of light in the medium
n₂₁refractive index of medium 2 with respect to medium 1

Worked example

The refractive index of a glass is 1.5. Find the speed of light in it.

Practice this conceptself-check · 4 quick reps

The same idea in a practice question:

Practice questionModerate

Example 1 · Light and Optics · Refraction and Lenses

A convex lens of power P is immersed in water. How will its power change?

Higher refractive index means faster light

It is the reverse:

v = \frac{c}{n}

, so the medium with the larger n is the one where light is slower.

Thinking water makes a lens stronger

A glass lens bends light less in water than in air, because glass and water differ less in refractive index. Its focal length grows, so its power falls.

Picking the pair with the largest indices

The bending depends on how much the two indices DIFFER. Going between n = 2.6 and n = 2.7 changes light less than going between 1.3 and 2.0.

Drill 2 more on refractive index and the bending of light

Concept 2 of 2: Convex and concave lenses, the lens formula and power

A convex lens is thicker in the middle and brings parallel rays together at its focus; a concave lens is thinner in the middle and spreads them out. Where the image forms depends on how far the object is from the lens compared with the focal length.

Definition

Convex lens: converging, positive focal length and power. Concave lens: diverging, negative.
Lens formula (distances measured from the lens; distances against the light are negative, so a real object has u negative): $\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$ .
Magnification $m = \dfrac{v}{u}$ ; a negative m means the image is inverted.
Power $P = \dfrac{1}{f}$ with f in metres; unit dioptre (D).
Convex lens, object at 2F: the image is at 2F on the other side, real, inverted and the same size. This is the only place where object and image are the same distance from the lens.
Convex lens, object at F: the rays come out parallel and the image is at infinity.

Lens formula, magnification and power

\frac{1}{v} - \frac{1}{u} = \frac{1}{f} \qquad m = \frac{v}{u} \qquad P = \frac{1}{f\,(\text{m})}

Worked example

An object is placed 15 cm in front of a convex lens of focal length 10 cm. Find where the image forms and its magnification.

Practice this conceptself-check · 4 quick reps

The same idea in a practice question:

Practice questionModerate

Example 2 · Light and Optics · Refraction and Lenses

In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens. A graph between the object distance u and the image distance v, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of

45^\circ

with the x - axis meets the experimental curve at P. The coordinates of P will be

Using centimetres in the power formula

Power needs the focal length in metres. A 20 cm lens has power

\frac{1}{0.2} = 5

D, not

\frac{1}{20}

Forgetting the sign of a concave lens

A concave lens has a negative focal length, so its power is negative. A lens of power

-2.5

D is concave.

Putting the same-size image at F

An object at F sends its image to infinity. The same-size image comes from an object at 2F, with the image at 2F.

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 (2)

Refractive index and the bending of light
Refractive index
$n = \frac{c}{v} \qquad n_{21} = \frac{n_2}{n_1} = \frac{v_1}{v_2}$
Convex and concave lenses, the lens formula and power
Lens formula, magnification and power
$\frac{1}{v} - \frac{1}{u} = \frac{1}{f} \qquad m = \frac{v}{u} \qquad P = \frac{1}{f\,(\text{m})}$

Watch out for (6)

Higher refractive index means faster light
→ Refractive index and the bending of light
Thinking water makes a lens stronger
→ Refractive index and the bending of light
Picking the pair with the largest indices
→ Refractive index and the bending of light
Using centimetres in the power formula
→ Convex and concave lenses, the lens formula and power
Forgetting the sign of a concave lens
→ Convex and concave lenses, the lens formula and power
Putting the same-size image at F
→ Convex and concave lenses, the lens formula and power

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