Question

A typical red blood cell subtends an angle of only 1.9 10 *⁻⁵ rad when viewed at a person’s near-point distance of 25 cm. Suppose a red blood cell is examined with a compound microscope in which the objective and eyepiece are separated by a distance of 12.0 cm. Given that the focal length of the eyepiece is 2.7 cm, and the focal length of the objective is 0.49 cm, find the magnitude of the angle subtended by the red blood cell when viewed through this microscope.

Answer 1

The magnitude of the angle subtended by the red blood cell when viewed through the microscope is approximately 7.8 * 10^-6 rad.

Step-by-step explanation:

To find the magnitude of the angle subtended by the red blood cell when viewed through the microscope, we can use the formula:

tanθ = (h/fo) + (h/fe)

Where θ is the magnitude of the angle, h is the height of the image formed by the objective lens, fo is the focal length of the objective lens, and fe is the focal length of the eyepiece.

Substituting the given values into the formula, we have:

tanθ = (h/0.49 cm) + (h/2.7 cm)

Since the distance between the objective and eyepiece is 12.0 cm, the total magnification of the microscope is given by:

M = fo/fe = 0.49 cm/2.7 cm

The height of the image formed by the objective lens can be found using the formula:

h = h' * M

where h' is the height of the object (red blood cell) when viewed at the near-point distance. Substituting the given values, we get:

h = (1.9 * 10^-5 rad) * 25 cm * (0.49 cm/2.7 cm)

Using a calculator, we can find that the magnitude of the angle subtended by the red blood cell when viewed through this microscope is approximately 7.8 * 10^-6 rad.