(a) Find the position and size of the virtual image formed when an object 2 cm tall is placed 20 cm from : (i) a diverging lens of focal length 40 cm. (ii) a converging lens of focal length 40 cm. (b) Draw labelled ray diagrams to show the formation of images in cases (i) and (ii) above (The diagrams may not be according to scale).

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Solution

$left parenthesis a right parenthesis space h subscript 1 equals space 2 c m u space equals space minus 20 c m left parenthesis i right parenthesis space f space equals space minus 40 c m left parenthesis D i v e r g i n g space L e n s right parenthesis 1 over v minus 1 over u space equals space fraction numerator 1 over denominator negative 40 end fraction 1 over v space equals space minus 1 over 40 minus 1 over 20 1 over v equals fraction numerator negative 3 over denominator 40 end fraction v space equals space minus 13.33 c m m space equals space v over u space equals space h subscript 2 over h subscript 1 fraction numerator negative 13.33 over denominator negative 20 end fraction space equals space h subscript 2 over h subscript 1 h subscript 2 space equals space 1.33 c m left parenthesis i i right parenthesis space f equals space 40 c m left parenthesis c o n v e r g i n g space l e n s right parenthesis 1 over v minus 1 over u space space equals 1 over f 1 over v minus fraction numerator 1 over denominator negative 20 end fraction space equals space 1 over 40 1 over v equals 1 over 40 minus 1 over 20 1 over v equals negative 1 over 40 v space equals space minus 40 c m m space equals space v over u equals h subscript 2 over h subscript 1 fraction numerator negative 40 over denominator negative 20 end fraction space equals space h subscript 2 over h subscript 1 h subscript 2 space equals space 4 c m$
(b)formation of image in case 1

Formation of image in case(ii):

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Similar questions

(a) An object is placed 10 cm from a lens of focal length 5 cm. Draw the ray diagrams to show the formation of image if the lens is (i) converging, and (ii) diverging. (b) State one practical use each of convex mirror, concave mirror, convex lens and concave lens.

Q. (a) Construct ray diagrams to illustrate the formation of a virtual image using (i) a converging lens, and (ii) a diverging lens.
(b) What is the difference between the two images formed above?

Q. A 2.0 cm tall object is placed 40 cm from a diverging lens of focal length 15 cm. Find the position and size of the image.

Q. (a) Draw ray diagrams to show the formation of a three times magnified (i) real image (ii) virtual image, of an object kept in front of a converging lens. Mark the positions of object, F, 2F, O and position of image clearly in the diagram.
(b) An object of size 5 cm is kept at a distance of 25 cm from the optical centre of a converging lens of focal length 10 cm. Calculate the distance of the image from the lens and size of the image.

(a) A small object is placed 150 mm away from a diverging lens of focal length 100 mm. (i) Copy the figure below and draw rays to show how an image is formed by the lens. (ii) Calculate the distance of the image from the lens by using the lens formula. (b) The diverging lens in part (a) is replaced by a converging lens also of focal length 100 mm. The object remains in the same position and an image is formed by the converging lens. Compare two properties of this image with those of the image formed by the diverging lens in part (a).

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(b)formation of image in case 1 Formation of image in case(ii):