A 6·cm tall candle is placed 225·cm from a lens with a focal length of +45·cm. N

Question

A 6·cm tall candle is placed 225·cm from a lens with a focal length of +45·cm. Note: enter the absolute value of your answers for all distances and heights ... use the signs to determine the type and orientation of the images.

(a) How far from the lens will the image be? cm.

(b) How tall will the image be? cm

(c) Which of the following describes the image? Choose all that apply. real virtual upright inverted Now, imagine that the candle is moved closer, so that it is only 18·cm from the lens.

(d) How far from the lens will the image be? cm.

(e) How tall will the image be? cm

(f) Which of the following describes the image? Choose all that apply. real virtual upright inverted

Explanation / Answer

Given: object distance (do) = -225 cm ; focal length (f) = 45 cm ; height of object (ho) = 6 cm

(a) using lens formula we have 1/di - 1/d0 = 1/f or 1/di = 1/45 - 1/225 = 180/225

So distance of the image (di) = 1.25 cm (real)

(b) magnification in lens is given by m = hi/ho = di/do or hi/6 = 1.25/-225 or hi = -0.033 cm (inverted image)

(c) The image will be real and inverted

Now object distance becomes (do) = -18 cm

(a) using lens formula we have 1/di - 1/d0 = 1/f or 1/di = 1/45 - 1/18 = -27/810 or di = -30 cm (virtual)

(b) magnification  m = hi/ho = di/do or hi/6 = -30/-18 or hi = 10 cm (upright image)

(c) The image will be virtual and upright in this case.

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