91Ó°ÊÓ

A magnifying glass is a convex lens used to magnify an object's image. Typically, the lens is housed in a frame with a grip.

• Power of the lens:\( - 4.00{\rm{ }}D\).
• Distance between lens and object: \(25.0\;cm\).

The focal length must first be calculated using the following equation:

\(f = \frac{1}{P}\)

Where \(f\)is the focal length of the lens and \(P\) is power.

The image distance \({d_i}\)is then determined using the lens equation

\(\frac{1}{f} = \frac{1}{{{d_i}}} + \frac{1}{{{d_o}}}\)

where \(f\) denotes the lens's focal length, \({d_o}\) denotes the distance between the object and the lens, and \({d_i}\) denotes the distance from the lens to the projected image that is in focus.

And the magnification \(m\) is computed using the equation,

\(m = \frac{{ - {d_i}}}{{{d_o}}}\)

where \(m\) denotes the magnification, \({d_o}\) denotes the distance between the object and the lens, and \({d_i}\) denotes the distance from the lens to the projected image that is in focus.

Substituting in the above equation, we get,

\(\begin{array}{c}m = \frac{{ - 1}}{{{d_o} \times \left( {P - \frac{1}{{{d_o}}}} \right)}}\\ = \frac{{ - 1}}{{0.25\;\;m \times \left( { - 4.00\;D - \frac{1}{{0.25\;\;m}}} \right)}}\\ = 0.25\;m\\ = \frac{1}{2}\end{array}\)

Therefore, the required solution is \(\frac{1}{2}\).