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Question

The distance between a real object and its image in a convex mirror of focal length 12 cm is 32 cm. Find the size of image if the object size is 1 cm.

A
23 cm
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B
13 cm
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C
1 cm
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D
14 cm
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Solution

Step 1: Given that:

Distance between object and image = 32cm

Focal length(f) of the convex mirror = +12cm

If u be the object distance and v be the image distance from the convex mirror then,

u+v=32cm

v=32u

Size of the object

(ho) = 1cm

Note: The focal length of a convex mirror is taken as positive as it lies right to the pole of the mirror.)

Step 2: Formula used:

The mirror formula is;

1v+1u=1f

Where u = object distance, v = image distance and f = focal length of the mirror

Magnification is given by;

m=hiho=vu

Step 3: Calculation of the object distance:

Using the mirror formula;

132u+1u=1+12cm

132u1u=112u(32u)u(32u)=112

2u3232uu2=112

2u×1232×12=32uu2

u232u+24u32×12=0

u28u384=0

(u224u)+(16u384)=0

u(u24)+16(u24)=0

(u24)(u+16)=0

When,(u24)0

(u+16)=0

u=16cm

Thus,

v=32(16cm)

v=48cm

Andif,(u+16)0

u=24cm

Thus,

v=3224cm

v=8cm

Step 4: Calculation of the size of the image:


For u= 24cm

hi1cm=48cm16cm

hi1cm=31

hi=3cm

And

for, u= 24cm

hi1cm=8cm24cm

hi=13cm

Thus,

the size of the image is 13cm .


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