Size of image of an object by a mirror having a focal length of 20 cm is observed to be reduced to 1/3 rd of its size. At what distance the object has been placed from the mirror? What is the nature of the image and the mirror?

The image of a candle flame formed by a lens is obtained on a screen placed on the other side of the lens. If the image is three times the size of the flame and the distance between lens and image is 80 cm, at what distance should the candle be placed from the lens? What is the nature of the image at a distance of 80 cm and the lens?

(i) One half of a convex lens of focal length 10 cm is converted with a black paper. Can such a lens produce an image of a complete object placed at a distance of 30 cm from the lens? Draw ray diagram to justify your answer.
(ii) A 4 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 20 cm. The distance of the object from the lens is 15 cm. Find nature, position and size of the image.

(a) Define focal length of a spherical lens.
(b) A divergent lens has a focal length of 30 cm. At what distance should an object of height 5 cm from the optical centre of the lens be placed so that its image is formed 15 cm away from the lens? Find the size of the image also.
(c) Draw a ray diagram to show the formation of image in the above situation.

(a) Define optical centre of a spherical lens.
(b) A divergent lens has a focal length of 20 cm At what distance should an object of height 4 cm from the optical centre of the lens be placed so that its image is formed 10 cm away from the lens. Find the size of the image also.
(c) Draw a ray diagram to show the formation of image in above situation.

(a) One - half of a convex lens is covered with a black paper. Will such a lens produce an image of the complete object? Support your answer with a ray diagram.
(b) An object 5 cm high is held 25 cm away from a converging lens of focal length 10 cm.
(i) Draw the ray diagram and
(ii) Calculate the position and size of the image formed.
(iii) What is the nature of the image?

(a) State the laws of refraction of light. Give an expression to relate the absolute refractive index of a medium with speed of light in vacuum.
(b) The refractive indices of water and glass with respect to air are 4/3 and 3/2 respectively. If the speed of light in glass is \({ 2\times 10 }^{ 8 }\) ms^-1, find the speed of light in (i) air, (ii) water.

A student wants to project the image of candle flame on the walls of school laboratory by using a lens:
(a) Which type of lens should he use any why?
(b) At what distance in terms of focal length 'F' of the lens should he place the candle flame so as to get
(i) a magnified, and 
(ii) a diminished image respectively on the wall?
(c) Draw ray diagram to show the formation of the image in each case.

(i) " A convex lens can form a magnified erect as well as magnified inverted image of an object placed in front of it. " Draw ray diagram to justify this statement stating the position of the object with respect to the lens in each case.
(ii) As object of height 4 cm is placed at a distance of 20 cm from a concave lens of focal length 10 cm. Use lens formula to determine the position of the image formed.

(a) Draw a ray diagram to show the formation of image by concave lens when an object is placed in front of it.
(b) In the above diagram mark the object -distance (u) and the image-distance (v) with their proper signs (=ve or -ve as per the new Cartesian sign convention) and state how these distance are related to the focal length (f) of the concave lens in this case.
(c) Find the nature and power of a lens which forms a real and inverted image of magnification -1 at a distance of 40 cm from its optical centre.