Question

To study a tissue sample better, a pathologist holds a \(5.00-\mathrm{cm}\) focal length magnifying glass \(3.00 \mathrm{~cm}\) from the sample. How much magnification can he get from the lens?

Short answer

Answer: The magnification provided by the magnifying glass is approximately 0.625 times.

Step-by-step solution

Write down the known values

We are given: Focal length of the magnifying glass (f) = 5.00 cm Distance between the lens and the tissue sample (u) = -3.00 cm (negative because the object is on the left side of the lens) We need to find the magnification (M).

Use the lens formula to find the image distance (v)

The lens formula is given by: \(\frac{1}{f} = \frac{1}{u} + \frac{1}{v}\) Plug in the given values of f and u: \(\frac{1}{5.00} = \frac{1}{-3.00} + \frac{1}{v}\) To solve for v, we can first find the common denominator and then solve for v: \(\frac{1}{5.00} + \frac{1}{3.00} = \frac{1}{v}\) \(v = \frac{1}{\frac{1}{5.00} + \frac{1}{3.00}}\)

Calculate the image distance (v)

Now, calculate the value of v by finding the sum of the fractions and taking the reciprocal: \(v = \frac{1}{\frac{1}{5.00} + \frac{1}{3.00}} = \frac{1}{\frac{8}{15}}\) \(v = \frac{15}{8}\) \(v \approx 1.875 \mathrm{~cm}\)

Use the magnification formula to find the magnification (M)

The magnification formula is given by: \(M = -\frac{v}{u}\) Plug in the values of v and u: \(M = -\frac{1.875}{-3.00}\)

Calculate the magnification (M)

Now, calculate the magnification (M): \(M = \frac{1.875}{3.00}\) \(M \approx 0.625\) So, the pathologist can get a magnification of approximately 0.625 times from the lens.