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Nature and reflection of light

Derivation 5. Set up a ratio
3. Consider the ray diagram setup of
Figure 4.30 From ABP :  A B P
11
(a) Place an object AB at a distance AB B P h v
1
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u from the pole. AB  BP  h i  u (1)
(b) The image A B forms at a 0
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1 1
distance v .  DEF :  A B F
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(c) The focal length f is the AB B F h v  f
1
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distance from P to F (principal DE  FE  h i  f (2)
focus). 0
6. Compare Equations (1) and (2) :

A D v  v  f
u f
B
1
C B F E P
vf  uv uf
vf  uv  uf
uv uv uv

A 1 f f
1
u  v
Figure 4.30: Geometry of a concave mirror

4. Identify similar triangles f   1  1    1
(a) (Triangle 1): △ABP (object  v u 
triangle) and AB P 11 (image 1 1 1
triangle) are similar v + u = f

(i)  APB  A PB 1 (from This equation applies to both concave
1
angle of incidence = angle and convex mirrors with both convention
of reflection). signs.

(ii) Both are right-angled.
Sign convention for the mirror equation
(b) (Triangle 2): △DEF (Mirror- Recall, the characteristics of images formed
focal triangle) and AB F by spherical mirrors depend on whether
11
(Image-focal triangle) are similar the mirror is concave or convex. The size,

(i)  EFD  B FA 1 position and nature of the image also
depend on the position of the object in
1
(Vertically opposite angles) front of the mirror. To determine the image
(ii) Both are right-angled. properties, there is a need to indicate the

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Physics Form 2 Final.indd 151 25/10/2025 10:27