Question

# Solve: (1) An object of size 7 cm is placed at 25 cm in front of concave mirror of focal length 15 cm. At what distance from the mirror should a screen be placed, so that we can get a sharp and clear image. Find nature and size of the image. (2) An object of height 5 cm is held 20 cm away from converging lens of focal length 10 cm. Find the position, nature and size of the image formed. (3) An object is placed at a distance of 10 cm from a convex lens of focal length 12 cm. Find the position and nature of the image.

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Solution

## (1) Given that: Object size, h1 = 7 cm Object distance, u = −25 cm Focal length of concave mirror, f = −15 cm Image distance, v = ? We have mirror formula, Screen should be placed at a distance of 37.5 cm from the pole to get a sharp focused image. Image has formed on the same side. So, it is real and inverted. Size of the image, (2) Given that: Height of the object, h1 = 5 cm Object distance, u = −20 cm Focal length of the converging (convex) lens, f = +10 cm Image distance, v =? Using lens formula, Image has formed on the other side of the object. So, it is real and inverted in nature. We know magnification (M) of a spherical lens can be given can be given in two forms: Note: Negative sign only indicated the inverted nature of image. So we can say, Height of the image, h2 = 5 cm (3) Given that: Object distance, u = −10 cm Focal length of the convex lens, f = +12 cm Image distance, v =? From lens formula, Image has formed at 60 cm away from the optical centre, on the same side of the object so it is virtual and erect in nature.

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