Lenses with given radii. Object O stands in front of a thin lens, on the central

Question

Lenses with given radii. Object O stands in front of a thin lens, on the central axis. For this situation, each problem in the table (below) gives object distance p, index of refraction n of the lens, radius r1 of the nearer lens surface, and radius r2 of the farther lens surface. (All distances are in centimeters.) Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real or virtual, (d) inverted from object O or noninverted, and (e) on the same side of the lens as object O or on the opposite side.

Explanation / Answer

using lens makers formula

1/f = (n - 1) [1/r1 - 1/r2]

1/f = (1.52 - 1) [1/(-17) - 1/(-29)]

f = - 79.01 cm

using the lens equation

1/f = 1/p + 1/i

1/(- 79.01) = 1/26 + 1/i

i = - 19.6 cm

m = magnification = - i/p = - (- 19.6) / 26 = 0.75

the image formed is virtual . since a diverging lens forms virtual image only

the image is not inverted.

the image is on same side of object

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