The lens equation in geometric optics is written: 1/p + 1/q = 1/f (a) Explain wh

Question

The lens equation in geometric optics is written:
1/p + 1/q = 1/f
(a) Explain what p, q and f represent in this equation. What does it indicate if the value of (i) f
is positive, (ii) q is negative? [4]
(b) The linear magnification of a lens is given by -q=p. With the aid of a sketch, provide a
simple trigonometric justification for this result. If the numerical value of the magnification
is found to be negative, what does that imply? [3]
(c) A converging lens with a focal length of 6 cm is going to be used as a magnifying glass.
Draw ray-tracing diagrams to show where the image will form if the object to be magnified
is placed (i) 7.5 cm, (ii) 4.5 cm in front of the lens. In each case also work out the image
distances using the lens equation, and the magnification achieved. [8]

Explanation / Answer

a) p and q are object and image distance while f equals the focal length. if the value of f is positive, then it is on the left side of the lens. if f is negative, then it is on the right side of the lens.
b) if the magnification is negative, then the image is small. if it's positive, it's bigger

c)mathematically:

(i) 1/7.5 + 1/q = 1/6

1/q = 1/30

q=30

p/q = 7.5/30

M= 0.25

ii)1/4.5 + 1/q = 1/6

1/q = -1/18

q = -18

p/q = 4.5/-18

M= -0.25

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