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Question

An object 4.0 cm in size, is placed 25.0 cm in front of a concave mirror of a focal length of 15.0 cm.

(i) At what distance from the mirror should a screen be placed in order to obtain a sharp image?

(ii) Find the size of the image.

(iii) Draw a ray diagram to show the formation of the image in this case.


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Solution

Step 1:Given:

Height of the object, h1=4cm

Distance of the object from the mirror, u=25cm

The focal length of the mirror, f=15cm

Step 2: (i) Finding the distance of the image (v) using the mirror formula:

We know that 1v+1u=1f

1v+1-25=1-151v=1-15+125=(-25+15)375=1-37.5cmv=37.5cm

The image is formed object side, 37.5cm from the pole of the concave mirror.

Step 3: (ii) Finding the height of the image h2 using the formula:

We know that H2H1=-uv

Where H1 is the size of the image .

Now, H24cm=-(-37.5cm)(-25cm)

H2=-4×37.525=-6cm

∴ size of image = 6cm

Step 4: (iii) The ray diagram showing the formation of the image in this case:


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