1. A object 5 mm Find . high is placed 600mm in front of a negative lens of focal length 250mm- ind (a) by calculation and (b) by graphical construction to scale, the position. size, and attitude (erect or inverted) of the image.

2. A lamp and screen are 1 m apart and a +7 D lens is mounted between them. Where can the lens be placed to give a sharp image, and what will be the magnification?

3. How does the transverse magnification produced by a lens of focal length I depend on the distance of the object from the lens? Calculate the focal length of the lens required to produce an image of a given object on a screen with a magnification of -3.5x, the object being situated -20 cm from the lens.

4. What is meant by the transverse (linear) magnification of an image? An object is placed -30mm from a positive lens and a virtual image four times the size of the object is required. Find graphically and by calculation the necessary focal length of the lens.

5. An object 1 cm long is placed perpendicular to the optical axis of a positive lens, the lower end of the object being 5 cm above a point on the axis 20cm from the lens. The lens has a focal length of 8 cm and an aperture of 3 cm. Find graphically the size and position of the image.

6. Apply carefully a graphical construction to find the position and size of the image of an object 2 mm high formed by a positive lens of focal length 25 cm. The object distance is (a) -50cm; (b) -80cm. Explain the reasons for the various steps in the construction.

7. A ray of light is incident in a direction inclined at 30° to the axis of a positive thin lens of 20 mm focal length, cutting the axis at a point 50 mm in front of the lens. A point moves along this ray from infinity on one side of the lens to infinity on the other. Find the conjugate ray graphically and trace the movement of the conjugate image point.

8. A lens of +6.55 D is 10cm in diameter and is fixed horizontally 24cm above a point source of light. Calculate the diameter of the circle of light projected on a ceiling situated 8.2 m above the lens.

9. Describe carefully how you would determine the focal length of a weak positive lens, say of 0.5 D power. Illustrate the method by giving a typical set of bench readings, and show how the focal length could be found from these.

10. An illuminated object A is placed at the first principal focus of a 20 D positive lens L, on the other side of which, at some distance, is a telescope which is adjusted until the object is seen distinctly. When a lens of unknown power is placed at the second principal focus of L, between L and the telescope, it is found necessary to move the object 2 cm further away from L in order to see it distinctly in the telescope. Calculate the power of the unknown lens.

11. A thin convergent lens gives an inverted image the same size as the object when the latter is 20 cm from the lens. An image formed by reflection from the second surface of the lens is found to be coincident with the object at 6 cm from the lens. Find the radius of curvature of the second surface of the lens and, assuming n= 1.5, the radius of curvature of the first surface.

12. A concave mirror is formed of a block of glass (it = 1.62) of central thikness 5cm. The front surface is plane and the hack surface, which is silvered, has a radius of curvature of 20cm. Find the position of the principal focus and the position of the image of an object 20cm in front of the plane surface.

13. Show that for a thin lens in air, the separation of the object and Image locations (the "throw") is given by OO' =f'(2- M - I/M) where ,f' is the hack focal length of the Iens and M the transverse (linear) magnification,

14. Show that for a fixed distance, d, between the object and the image, there are two positions of the lens giving different object/image distances if the focal length of the lens f'

15. A Galilean telescope consists of a +4 D lens and a -6 D lens in air. Find the separation of the two lenses if the system is to be afocal (light from a distant object is imaged at infinity). Repeat the calculation if the second lens has a power of +6D (this is a keplerian telescope) and hence show that, in both cases, the separation of the, lenses is the sum of the fool lengths