1) An 28.9 cm long pencil is placed along the principal axis of a convex mirror

Question

1) An 28.9 cm long pencil is placed along the principal axis of a convex mirror (focal length 65.5 cm), If the end of the pencil nearest to the mirror is 5.53 cm from the vertex of the mirror (within the focal point): find the length, in cm, of the image.

2) An object at distance 59.3 cm from a convex lens creates a real image 16.7 cm from the lens. Find the focal length of this lens, in cm.

3) An object of height H at distance 88.3 cm from a concave lens creates a virtual image of height H/3.62. Find the focal length of this lens, in cm.

Explanation / Answer

1)Given,

h = 28.9 cm ; o = 5.53 cm ; f = -65.5 cm

we know from lens eqn

1/f = 1/i + 1/o

i = o x f/(o - f) = 5.53 x -65.5/(5.53 - (-65.5)) = 362.215/71.03 = -5.09 cm

i = -5.09 cm

M = -i/o = h'/h

h' = M h = -(-5.09)/5.53 x 28.9 = 26.60 cm

Hence, h' = 26.60 cm

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