In a compound microscope, the image formed by the objective lens is at a distance of 3.0cm from the eye lens. If the final image is at 25.0cm from the eye lens, calculate the focal length of the eye lens
To find the focal length of the eye lens in a compound microscope, we use the lens formula:
\(\frac{1}{f} = \frac{1}{v} - \frac{1}{u}\)
Given: Image distance from the eye lens: \( v_2 = 25.0 \, \text{cm}\)
Object distance for the eye lens (image from the objective lens): \( u = -3.0 \, \text{cm} \) (negative since it is on the same side as the incoming light)
\(\frac{1}{f} = \frac{1}{25.0} - \frac{1}{-3.0}\)
\(\frac{1}{f} = \frac{1}{25.0} + \frac{1}{3.0}\)
\(\frac{1}{25.0} = 0.04 \quad \text{and} \quad \frac{1}{3.0} \approx 0.3333\)
\(\frac{1}{f} = 0.04 + 0.3333 \approx 0.3733\)
\(f \approx \frac{1}{0.3733} \approx 2.68 \, \text{cm}\)
The focal length of the eye lens is approximately \( 2.68 \, \text{cm} \).
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