Question

Discuss about simple microscope and obtain the equations for magnification for near point focusing and normal focusing.

Answer 1

1. 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.
2. 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.
3. 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"`
4. With the help of lens equation,
   `1/"v" − 1/"u" = 1/"f"` the magnification can further be written as,
   m = 1 – `"v"/"f"`
5. Substituting for v with sign convention,
   v = -D
6. m = `1 + "D"/"f"`
   This is the magnification for near-point focusing.
   
   Near point focusing
7. The angular magnification is defined as the ratio of angle θ_i 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
8. For unaided eye shown in Figure (a),
   tan θ₀ ≈ θ₀ = `"h"/"D"`
9. For aided eye shown in Figure (b),
   tan θ_i ≈ θ_i = `"h"/"f"`
10. The angular magnification is,
    m = `θ_"i"/θ_0` = `("h"//"f")/("h"//"D")`
    m = `"D"/"f"`
    This is the magnification for normal focusing.