if y and y/4 are objects and images distance duc to convert lens respectively, then focal length is 14y and 22y

Verified answer

Answer:

The focal length is

[tex] \frac{ - y}{3} \: unit[/tex]

Explanation:

Given Object distance from the lens is y

and image distance from the lens is y/4

Here lens is a convex lens.

We know for convex lens,

[tex] \frac{1}{v} - \frac{1}{u} = \frac{1}{f} .........(1)[/tex]

Here,

[tex]u = image \: distance \\ v = object \: distance \\ and \: f = focal \: length[/tex]

From (1),

[tex] \frac{1}{y} - \frac{1}{ \frac{y}{4} } = \frac{1}{f} [/tex]

[tex] \frac{1}{y} - \frac{4}{y} = \frac{1}{f} [/tex]

[tex] \frac{ - 3}{y} = \frac{1}{f} [/tex]

So,

[tex]f = \frac{ - y}{3} [/tex]

Required focal length is

[tex] \frac{ - y}{3} \: unit[/tex]