Question

A 4.00-cm tall light bulb is placed a distance of 40 cm from a concave mirror having a focal length of 16 cm. Determine the image distance

Answer 1

Given:-

• Object height ,ho = 4cm
• focal length ,f = -16cm
• Object distance ,u = -40cm

To Find:-

• Image distance ,v

Solution:-

According to the Question

We need to calculate the image distance of the bulb . Using mirror formula .

• 1/v + 1/u = 1/f

where,

• v is the Image Position
• u is the object distance
• f is the focal length

Substitute the value we get

$:\implies$ 1/v + 1/(-40) = 1/-16

$:\implies$ 1/v -1/40 = -1/16

$:\implies$ 1/v = -1/16 + 1/40

$:\implies$ 1/v = -5+2/80

$:\implies$ 1/v = -3/80

$:\implies$ v = -80/3

$:\implies$ v = -26.66 (approx)

• Hence, the image distance is 26.66 cm from the mirror .

Answer 2

Given :-

A 4 cm  tall light bulb is placed a distance of 40 cm from a concave mirror having a focal length of 16 cm.

To Find :-

Image distance

Solution :-

We know that

1/u + 1/v = 1/f

1/-40 + 1/v = 1/-16

-1/40 + 1/v = -1/16

1/v = -1/16 - (-1)/40

1/v = -1/16 + 1/40

1/v = -5 + 2/80

1/v = -3/80

v = -80/3

Hence

Image distance = -80/3 cm

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