3. Worked Examples
Example 1: Find Focal Length
An object is 30 cm from a mirror. The image forms at 15 cm. Find focal length.
1 Use formula: 1/v + 1/u = 1/f
2 Put values: 1/(-15) + 1/(-30) = 1/f
3 Solve: -1/15 - 1/30 = -3/30 = -1/10
Answer: f = -10 cm (concave mirror)
Example 2: Find Image Distance (Lens)
Object is at 20 cm from convex lens. Focal length is 10 cm. Find image.
1 Use formula: 1/v - 1/u = 1/f
2 Put values: 1/v - 1/(-20) = 1/10
3 Simplify: 1/v + 1/20 = 1/10
4 Solve: 1/v = 1/10 - 1/20 = 1/20
Answer: v = 20 cm on other side
Example 3: Find Power of Lens
Focal length is 25 cm = 0.25 m. Find power.
1 Use formula: Power = 1/f
2 Put value: P = 1 / 0.25
3 Calculate: P = 4
Answer: Power = +4 D (convex lens, positive)
5. Take-Home Handout
Part A: Fill in the Blanks
1. Light travels in __________ lines.
2. Angle of incidence equals angle of __________.
3. A concave mirror curves __________ like a bowl.
4. Light bending in a new material is __________.
5. Power of a lens is measured in __________.
Part B: True or False
1. Light always travels in curved lines.
2. A convex mirror makes images bigger.
3. Refraction happens when light changes material.
4. A concave lens is thick in the middle.
5. Diamond has a high refractive index.
Part C: Solve These Problems
1. Object is 40 cm from a concave mirror. Image forms at 20 cm. Find focal length.
2. Convex lens has focal length 15 cm. Object at 30 cm. Find image distance.
3. A lens has focal length 50 cm. Find its power in dioptres.
Part D: Match the Columns
| Column A | Column B |
| 1. Concave mirror | a. Spreads light rays apart |
| 2. Convex mirror | b. Thick in the middle |
| 3. Convex lens | c. Used in car side mirrors |
| 4. Concave lens | d. Curves inward like a bowl |
| 5. Refractive index | e. Shows how much light bends |
Write your answers: 1-__, 2-__, 3-__, 4-__, 5-__
Part E: Draw and Label
Draw a ray diagram for a convex lens. Show the object, image, focus (F), and optical center (O).
✅ Detailed Solutions – Section 5 Handout
Part A: Fill in the Blanks
1 Light travels in straight lines.
2 Angle of incidence equals angle of reflection.
3 A concave mirror curves inward like a bowl.
4 Light bending in a new material is called refraction.
5 Power of a lens is measured in dioptres (D).
Part B: True or False
1 False. Light always travels in straight lines, not curved.
2 False. A convex mirror makes images smaller and upright, not bigger.
3 True. Refraction occurs whenever light moves from one material to another.
4 False. A concave lens is thin in the middle, not thick.
5 True. Diamond has one of the highest refractive indices of any natural material.
Part C: Solved Problems
Problem 1 — Object 40 cm, image 20 cm from a concave mirror. Find focal length.
1 Both object and image are in front of the mirror, so u = −40 cm and v = −20 cm.
2 Use mirror formula: 1/f = 1/v + 1/u.
3 1/f = 1/(−20) + 1/(−40) = −2/40 − 1/40 = −3/40.
f = −40/3 ≈ −13.3 cm (concave mirror, negative focal length).
Problem 2 — Convex lens f = 15 cm, object at 30 cm. Find image distance.
1 Object is on the left, so u = −30 cm. f = +15 cm.
2 Lens formula: 1/v − 1/u = 1/f.
3 1/v − 1/(−30) = 1/15 → 1/v + 1/30 = 1/15.
4 1/v = 1/15 − 1/30 = 2/30 − 1/30 = 1/30.
v = 30 cm. Image forms 30 cm on the other side of the lens (real, inverted, same size).
Problem 3 — Lens with focal length 50 cm. Find power.
1 Convert: f = 50 cm = 0.50 m.
2 P = 1/f = 1/0.50 = 2.
Power = +2 D (positive, so it is a convex lens).
Part D: Match the Columns
1 Concave mirror → d. Curves inward like a bowl
2 Convex mirror → c. Used in car side mirrors
3 Convex lens → b. Thick in the middle
4 Concave lens → a. Spreads light rays apart
5 Refractive index → e. Shows how much light bends
Part E: Ray Diagram – Convex Lens (Description)
1 Draw a horizontal principal axis. Place a convex lens (ellipse) at the centre point O.
2 Mark F on both sides of the lens at equal focal length distances. Mark 2F further out.
3 Place an upward arrow (object) beyond 2F on the left.
4 Ray 1: parallel to axis → bends through F on the right. Ray 2: through optical centre O → goes straight.
Where the two rays meet on the right side is the image location — real and inverted.
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