Examples on lens and combination OF lens and mirror

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Power Of Combination Of Lens

A concave mirror of focal length 20 cm and a convex lens of focal length 10 cm are kept with their optic axes parallel but separated by 0.5 mm as shown in the figure. The distance between the the lens and mirror in 10 cm. An object of height 3 mm is placed on the optic axis of lens at a distance between the lens and mirror is 10 cm. An object of height 3 mm is placed on the optic axis of lens at a distance 15 cm from the lens. Find the length of the image formed the mirror in mm.

A thin convex lens of focal length 30 cm is placed in front of a plane mirror. An object is placed at a distance x from the lens (not in between lens and mirror ) so that its final image coincides with itself. Then, the value of x is

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A thin convex lens of focal length 'f' is put on a plane mirror as shown in the figure . When an object is kept at a distance 'a' from the lens - mirror combination , its image is formed at a distance (a)/(3) in front of the combination . The value of 'a' is :-

A 20cm convex lens is placed in contact with a diverting lens of unknown focal length ,The lens combination acts as a converging lens and has a length of 30cm .What is the focal length of the diverging lens.