Question

In a compound microscope, let u₀ and v₀ be the object distance and image distance respectively. The objective of focal length f₀ magnifies a tiny object into a real, inverted image. The linear magnification of the objective is ______.

विकल्प

• `(f_0 + u_0)/(u_0f_0)`

• `(u_0f_0)/(f_0 + u_0)`

• `f_0/(f_0 + u_0)`

• `u_0/(u_0f_0 + 1)`

Answer 1

In a compound microscope, let u₀ and v₀ be the object distance and image distance respectively. The objective of focal length f₀ magnifies a tiny object into a real, inverted image. The linear magnification of the objective is `underlinebb(f_0/(f_0 + u_0))`.

Explanation:

The linear magnification objective lens is

`m_0 = "v"_0/u_0` ....................(i)

Using lens formula, `1/"v"_0 - 1/u_0 = 1/f_0`

⇒ `1/"v"_0 = 1/f_0 + 1/u_0 = (u_0 + f_0)/(u_0f_0)` or `"v"_0 = (u_0f_0)/(f_0 + u_0)`

Putting this value in Eq. (i), we get

`m_0 = f_0/(f_0 + u_0)`