well, its a simple one....
we know that min. distance between a real object and its real image is 4f.
so, option (b) is correct.
well, option (a) should also be correct,
because if d>4f...then naturally it is greater than 2f
let distance of object from lens be x
so, image distance= d - x
on applying, lens formula...we will get a quadratic in x.
which will give two positions of lens.
x= {d+(d2-4df)1/2}/2 and {d-(d2 -4df)1/2}/2
so, M1 = -{d+(d2-4df)1/2}/{d-(d2 -4df)1/2}
and M2 = -{d-(d2 -4df)1/2}/{d+(d2-4df)1/2}
so, M1M2 = 1
hence option (c) is also correct..
Lokesh,whatever you have done is perfectly alright.But can you please explain why question says that sharp images are formed?
Lets go with definition of a real image...
"A real image is formed where the light rays actually meet"
practically, if an object is kept at fixed distance from lens, then, there will be infinite no. of pts where light rays are meeting ..so,screen can be placed at infinite no. of points to obtain an image, but all images will be blurred except at one particular position of screen where maximum no. of light rays are actually meeting....and that particular position is mathematically find out by lens formula..
so, images are formed at infinite points but for a fixed object distance, there will be only one position where sharp image is formed,while blurred images are formed at rest of points.
It will be more clear to you if you understand it practically...
"take a normal convex lens, try to focus image of a distant object like tree outside the window on a white screen(or wall), you will find that images will be formed at many positions but a sharp(clear) image is formed only at one particular position(when lens is at distance=focal length, from screen)"
I hope now it will be clear to you...
