The magnifying power of a simple microscope when the final image is formed at D = 25 cm from eye is :(f is the focal length)

Step 1: Given data -

The final image is formed at D=25 cm

As the convex lens is used in the simple microscope and the object is between the optical center and the focus, thus, the image is formed on the same side of the lens where the object is.

By the sign conventions,

The final image is formed at v=-D=-25 cm

Step 2: Formula used -

According to the lens formula,

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

Where u is the distance of the object, v is the distance of the image from the optical center, and f is the focal length,

The magnifying power of the lens in terms of u and v is,

$m=\frac{v}{u}$

Step 3: Calculating the magnifying power of the lens -

By substituting the value of distance of the object in the lens formula, we get,

$\frac{1}{-D}-\frac{1}{u}=\frac{1}{f}$

Multiplying both side by D, we get,

$\frac{D}{-D}-\frac{D}{u}=\frac{D}{f}$

By substituting the value of distance of the object in magnifying power formula,

$m=\frac{-D}{u}$

From equation (1) and (2),

$m=1+\frac{D}{f}$

Thus, the magnifying power of the simple microscope in the given case is $1+\frac{D}{f}$

Hence, option B is the correct answer.