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Question
Discuss about simple microscope and obtain the equations for magnification for near point focusing and normal focusing.
Solution
- A simple microscope is a single magnifying (converging) lens of small focal length The idea is to get an erect, magnified and virtual image of the object.
- Near point focusing –
The image is formed at near point, i.e. 25 cm for normal eye. This distance is also called as least distance D of distinct vision. In this position, the eye feels comfortable but there is little strain on the eye. - Normal focusing –
The image is formed at infinity. In this position the eye is most relaxed to view the image.
> Object distance u is less than f. The image distance is the near point D. The magnification m is given by the relation,
m = `"v"/"u"` - With the help of lens equation,
`1/"v" − 1/"u" = 1/"f"` the magnification can further be written as,
m = 1 – `"v"/"f"` - Substituting for v with sign convention,
v = -D - m = `1 + "D"/"f"`
This is the magnification for near-point focusing.
Near point focusing - The angular magnification is defined as the ratio of angle θi subtended by the image with an aided eye to the angle θ0 subtended by the object with the unaided eye.
m = `theta_"i"/theta_0`
Normal focusing - For unaided eye shown in Figure (a),
tan θ0 ≈ θ0 = `"h"/"D"` - For aided eye shown in Figure (b),
tan θi ≈ θi = `"h"/"f"` - The angular magnification is,
m = `θ_"i"/θ_0` = `("h"//"f")/("h"//"D")`
m = `"D"/"f"`
This is the magnification for normal focusing.
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