Question

an optical instrument consist of two lenses .if the object distance for lens 1 is 12cm then the image distance is 36cm.if the height of the object for lens 2 is 5cm then the image height is 2.5cm. evaluate the combined magnification of the two lenses

Answer 1

The magnification of first lens can be given as,

`m_1=-(v_1)/(u_1)`

Here, m1 is the magnification of first lens, v1 is the distance of image from first lens and u1 is the distance of object from first lens.

Substitute the known values in the equation,

`\begin{gathered} m_1=-\frac{36\text{ cm}}{12\text{ cm}} \\ =-3 \end{gathered}`

The magnification of second lens can be given as,

`m_2=-(v_2)/(u_2)`

Here, m2 is the magnification of second lens, v2 is the distance of image from second lens and u2 is the distance of object from second lens.

Substitute the known values in the equation,

`\begin{gathered} m_2=-\frac{2.5\text{ cm}}{5\text{ cm}} \\ =-0.5 \end{gathered}`

The combined magnification of two lenses can be given as,

`m=m_1m_2`

Substitute the known values,

`\begin{gathered} m=(-3)(-0.5) \\ =1.5 \end{gathered}`

Thus, the combined magnification of two lenses is 1.5.