Physics · Lesson 31

Practical 4: glass block, converging lens and concave mirror

WAECNECO

What the syllabus asks

WAEC: refraction through a rectangular glass block (Snell’s law, refractive index, lateral displacement), converging lens (focal length by the lens formula; power), concave mirror (focal length by no parallax). Links to p-units on reflection, refraction and lenses.

NECO: refraction through a rectangular glass block (Snell’s law, refractive index, lateral displacement), converging lens (focal length by the lens formula; power), concave mirror (focal length by no parallax). Links to p-units on reflection, refraction and lenses.

What you will learn

Determine the refractive index of glass using pins and Snell’s law.
Determine the focal length of a converging lens with a screen.
Determine the focal length of a concave mirror by no parallax.
Choose and plot the correct straight-line graphs for light experiments.
Read slopes and intercepts in optics graphs with signs and units.
State precautions and sources of error for optics experiments.
Answer part (b) items on the laws of refraction and reflection and lens calculations.
Handle optics diagrams in the alternative-to-practical paper.

Key points

Glass block: sin i against sin r; slope = n; sample n = 1.52.
Angles from the normal; pins vertical and well apart; sight the bases.
Lens: rough f first; sharpest image; u and v from the lens centre.
1/v against 1/u: slope −1, intercepts 1/f; sample f = 15.0 cm.
uv against (u + v): slope f.
Mirror: no parallax; sample f = 10.0 cm, r = 20.0 cm.
Critical angle: sin C = 1/n.
Power P = 1/f (m) in dioptres.
Attach traces; label pins and rays.
Sense-check every result.

Start here: Concept summary: the three light experiments

Light questions in WAEC Paper 3 and NECO Paper I are popular because the apparatus is cheap and the readings come quickly: a rectangular glass block with optical pins on drawing paper, a converging lens on a metre rule with a lit object and a screen, and a concave mirror with an object pin and a search pin. All three test the same skills as mechanics: careful readings, a neat table, a straight-line graph and a deduced constant, plus a part (b) on the laws of refraction or reflection.

In this unit:

the glass block gives the refractive index n from Snell’s law, sin i = n sin r;
the converging lens gives the focal length f from the lens formula, 1/u + 1/v = 1/f;
the concave mirror gives f from the same formula, using the no-parallax method.

Sign convention. WAEC questions use the "real-is-positive" convention: distances of real objects and real images are positive, and the focal length of a converging lens or a concave mirror is positive. In every experiment here the object and image are real, so u, v and f are all positive and the formula is simply 1/u + 1/v = 1/f. (Some textbooks use the Cartesian convention instead. If a question gives a formula, use it as given.)

Two optical habits run through this unit. First, pins must be vertical and well separated, because the line through two pins is only as accurate as their spacing allows. Second, an image position is found where it is sharpest or where there is no parallax, and you must move the screen or search pin back and forth through that position to locate it, rather than stopping at the first place that looks acceptable.

Continue this lesson in the free app →

Practice questions

1. For i = 60° a student records r = 35°. Find n from this row.

Show worked answer

n = sin 60°/sin 35° = 0.866/0.574 = 1.51.

2. Why is sin i plotted against sin r rather than i against r?

Show worked answer

Snell’s law makes sin i proportional to sin r, giving a straight line through the origin with slope n; i and r are not proportional.

3. Calculate the critical angle of glass with n = 1.50.

Show worked answer

sin C = 1/1.50 = 0.667; C = 41.8°.

4. State two precautions in the glass block experiment.

Show worked answer

Pins vertical and at least 5 cm apart; sight the bases of the pins; replace the block exactly on its outline; draw the normal accurately.

5. u = 24.0 cm and v = 40.0 cm for a converging lens. Find f and the power.

Show worked answer

f = uv/(u+v) = 960/64.0 = 15.0 cm; P = 1/0.150 = 6.67 D.

Key words

Normal: Line perpendicular to a surface at the point of incidence.
Angle of incidence: Angle between incident ray and normal.
Refractive index: sin i / sin r, or speed in air ÷ speed in medium.
Lateral displacement: Sideways shift of a ray passing through a parallel block.
Critical angle: Angle in the denser medium for which the refracted angle is 90°.
Principal axis: Line through the optical centre (or pole) and the centres of curvature.
Principal focus: Point where paraxial parallel rays meet after refraction or reflection.
Focal length: Distance from optical centre or pole to principal focus.
Power of a lens: 1/f in metres; unit dioptre.
No parallax: No relative motion between two objects as the eye moves.
Centre of curvature: Centre of the sphere of which the mirror is part.
Real-is-positive: Sign convention: real distances positive, virtual negative.

Learn Practical 4: glass block, converging lens and concave mirror step by step, free.
The Cara's Tips app teaches every topic from the very basics, with quick checks, worked examples and exam practice. It works offline.
Open this lesson in the free app Download for Android