a. A single bi-convex lens (a lens with two convex surfaces) made of sapphire (i

Question

a. A single bi-convex lens (a lens with two convex surfaces) made of sapphire (index of refraction n = 1.77) has surfaces with radii of curvature r1 = 24.0 cm and r2 = -24.0 cm. What is the focal length of the lens in air?

b. If an object is placed at p = 37.8 cm from the lens, where is the image? (Use plus sign for a real image, and minus sign for a virtual image.)

c. If the object has a height of h = 1.70 cm, how large is the image? (Use plus sign for an upright image, and minus sign for an inverted image.)

Explanation / Answer

For thin lenses,
1/f = (n - 1) [1/R1 - 1/R2]
1/f = (1.77 - 1) [1/24 + 1/24]
1/f = .77*1/12
f = 15.58 cm.

b)

p=object distance
q=image distance
f=focal length
1/p+1/q=1/f

1/q = 1/15.58 - 1/37.8

q = 26.5 cm

c)

hi/ho = q/p

=> hi = (26.5/37.8)*1.7 = 1.1918 cm

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