Question

6. Find the focal length of a convex lens is 10cm. A candle of height 12cm is placed at a distance
of 20cm from that lens. The position, nature and length of image of candle.
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Answer 1

The image is 20 cm away from the lens on principal axis in inverted position. The length of image is same as height of object, 12 cm. The image is real image with magnifiacation is 1.

Explanation:

Given:

           distance of object from lens 'u' = 20 cm

           focal length of convex lens 'f' = 12 cm

To find:

           We need to find the distance of image from lens, it's position , it's    nature and length of image.

Solution:

              Se know the lens formula,

                                   ⇒ $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$

                                    ⇒  $\frac{1}{v} = \frac{1}{f} - \frac{1}{u}$

          putting values,

                                       ⇒ $\frac{1}{v} = \frac{1}{10} - \frac{1}{20}$

                                       ⇒ v = -20 cm

Negetive sign shows that is is inverted in nature and it's a real image as it is in the right side (in image side).

Magnification 'm',

                                       ⇒  m = $\frac{v}{u}$

                                        ⇒  m = $\frac{-20}{20}$ = 1

So, image is of same size as object which is 20 cm.

The image is at the centre of curvature of right side of the convex lens in inverted position.