A converging lens (f = 26.1 cm) is used to project an image of an object...

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A converging lens (f = 26.1 cm) is used to project an image of an object...

A converging lens (f = 26.1 cm) is used to project an image of an object onto a screen. The object and the screen are 114 cm apart, and between them the lens can be placed at either of two locations. Find the two object distances. (Enter your answers from smallest to largest.) cm cm

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Answer 1

Answer #1

We know that,

1/f = 1/O +1/i

or f = Oi/O+i = 26.1 = Oi/114

Oi = 26.1*114 =2975.4

O+i = 114

Then,

(O+i)² = O² +i² +2(Oi) =O² +i² +2(2975.4 ) =12996

So,O² +i² = 7045.2

Now , (O-i)² = O² +i² -2(Oi) = 7045.2 - 2(2975.4 ) = 1094.4

O-i = 33.08 cm and O+i = 114

so, i= 40.46 cm and O= 73.54 cm

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Answer 2

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A converging lens (f = 26.1 cm) is used to project an image of an object...

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