A candle and a screen are placed 90 cm apart. Steve placed a lens between them such that a clear image is formed on the screen and the image is twice the size of the object.
(a) Which type of lens is used by Steve?
(b) Write an equation relating the object distance u, image distance v, and the distance between the candle and the screen.
(c) State the ratio between the image distance v and the object distance u.
(d) Calculate the image distance.
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(a) A clear image is obtained on a screen, so the image is real and magnified. Only a convex lens can form a real and magnified image.
Hence, Steve used a convex lens.
(b) The candle and the screen lie on opposite sides of the lens, so the sum of the two distances is equal to the separation between them.
u + v = 90 cm
(c) The image is twice the size of the object, so its image distance is twice its object distance.
Hence, v : u = 2 : 1
(d) From part (c), v = 2u
Substituting in u + v = 90, we get
$$\begin{aligned}\text u + 2\text u = 90 \\[1em] \Rightarrow 3\text u = 90 \\[1em] \Rightarrow \text u = 30 \text { cm}\end{aligned}$$
Then,
v = 90 − 30 = 60 cm
Hence, the image distance is 60 cm.