DSE Physics | Lenses Lesson-Prep Guide (Tutor Edition) | Imaging Formula, Magnification and Dioptres

2026-11-01

Tutor lesson-prep guides · Secondary Physics

Students can recite 1/f = 1/u + 1/v but fall apart on the signs: virtual images marked real, magnification upside down. This lesson does three things only: fix the signs, draw the rays, check the answer.

Objectives — Students can (1) use 1/f = 1/u + 1/v to find the image distance and decide real or virtual; (2) use m = v/u for magnification and orientation; (3) convert focal length to dioptres and explain which lens corrects myopia and hyperopia.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Reciprocals	What is 1/10 minus 1/15	1/30
Units	What must you do before adding 15 cm and 0.1 m	Convert to one unit
Similar triangles	Are the side ratios of similar triangles equal	Yes, same ratio

02 Lesson flow (60 minutes)

Time	Stage	Tutor does	Student does
0-8 min	Sign rules	f positive for convex, u positive, v positive for real	Write the three rules
8-22 min	Imaging formula	Substitute, take reciprocals, decide real or virtual	v = 30 cm
22-34 min	Magnification	m = v/u, sign shows inversion	m = 2
34-44 min	Ray diagram	Parallel ray through focus, centre ray straight, focus ray parallel	Draw the image
44-54 min	Power and correction	P = 100/f(cm), concave for myopia	10 D
54-60 min	Exit check	Three questions marked on the spot	Work independently

03 Teaching script (read it out)

Scene 1: Fix the signs before the formula

For a convex lens f = +10 cm and object distance u is always positive. A positive v means a real image on the far side and inverted; a negative v means a virtual, upright image on the same side as the object.
Example: u = 15 cm, 1/v = 1/10 – 1/15 = 0.0333 per cm, so v = 30 cm and the image is real.

Ask students: what is v when u = 30 cm (15 cm, still real but diminished)?

Scene 2: Magnification and the meaning of inverted

m = v divided by u. With u = 15 cm and v = 30 cm, m = 2: the image is 2 times taller and inverted.
With u = 5 cm, less than f, 1/v = 1/10 – 1/5 gives v = -10 cm: negative, so virtual, upright and magnified by 2. That is a magnifying glass.
Pattern: u above 2f gives a diminished real image; f to 2f gives a magnified real image; u below f gives a magnified virtual image; u equal to f gives no image.

Ask students: why is there no image when u equals f? (The emerging rays are parallel, so the image is at infinity.)

Scene 3: Power is just another way to write focal length

Power P in dioptres is 100 divided by f in centimetres. f = 10 cm gives P = 10 D, a converging lens used for hyperopia and presbyopia.
A myopic eye focuses in front of the retina, so a diverging lens spreads the rays first and the power is written negative. A shop label of -2.00 D means a concave lens of focal length 50 cm.

Reminder: the formula uses f in centimetres, not metres; the unit error costs a factor of 100.

04 Question types and worked steps

Type	Example	Steps	Answer
Calculation	Find v from u and f	1/v = 1/f – 1/u then check the sign	v = 30 cm
Calculation	Magnification	m = v divided by u	2x
Decision	Real or virtual	v positive means real	Negative means virtual and upright
Application	Power and correction	P = 100 divided by f in cm	10 D

Sanity check (teach this): For a convex lens and a real object, u above f must give a real image with positive v; u below f must give a virtual image with negative v. If u is above f but v comes out negative, the subtraction order was reversed. Magnification grows with image distance, and m is exactly 1 at u = 2f.

05 Independent practice (3 questions)

Question	Answer	What to watch
Image distance for f = 10 cm and u = 15 cm	30 cm, real	Take reciprocals last
Magnification in the same case	2	m = v divided by u
Power of a lens with f = 10 cm	+10 D	P = 100 divided by f in cm

06 Common mistakes and what to say

Mistake	Student writes	Say this
Subtraction reversed	1/v = 1/u – 1/f gives v = -30 cm	Focal term always comes first: 1/f minus 1/u.
Virtual called real	u = 5 cm answered as v = 10 cm real	Keep the minus sign: negative means virtual and upright.
Magnification inverted	Answered m = 0.50	m is image distance over object distance.
Wrong unit in power	f = 0.1 m put into 100/f gives 1000 D	The formula takes f in centimetres.

07 Homework (paper, section and question numbers)

DSE Physics practice paper (optics) — Section B lens calculation
Secondary Physics chapter index — All chapters

08 Exit check (last 5 minutes)

Question	Answer	Decision
Image distance for f = 10 cm and u = 30 cm	15 cm	Three correct means move on to optical instruments
Nature of the image when u = 5 cm	Virtual, upright, magnified	One wrong means re-teach the signs
Power of a lens with f = 10 cm	+10 D	Two or more wrong means restart act one

09 Tutor FAQ

Must students memorise four image cases?

No. Use the relation between u and f and substitute; the case follows.

Can a virtual image be projected on a screen?

No. The emerging rays only appear to meet when extended backwards.

What sign does a concave lens focal length take?

Negative. Substituting it always gives a negative v, so the image is always virtual.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.