Figure, shows variation of magnification m (produced by a thin convex lens) and distance v of image from pole of the lens. When of the following statements are correct?

Options

A. Focal length of the lens is equal to intercept on v-axis
B. Focal length of the lens is equal to inverse of slope of the line
C. Magnitude of intercept on m-axis is equal to unity
D. None of the above

Answer

a.,b.,c.

Explanation

`(1)/(v)-(1)/(u)=(1)/(f)`
`1-(v)/(u)=(v)/(f)` (i)
Since m is positive in the given figure, therefore m represents magnitude of the magnification. In fact, if a real image is formed by a convex lens, then the image and object will be on opposite sides of the lens. It means, if v is positive, then u will be negative .
Therefore,
`m=|(v)/(u)|=-(v)/(u)` (ii)
Hence, Eq. (i) becomes
`m=v/(f)-1`
It means, the graph between m and v will be a straight line having intercept `-1` on m-axis and slope of the ling `tantheta` is equal to `(1//f)`. Hence, option (b) and (c) are correct. Putting `m=0` in Eq. (ii), `v=f` . Hence (a) is also correct. Obviously, (d) is wrong.