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Answer in Brief

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

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#### 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. For this the object is placed between F and P on one side of the lens and viewed from other side of the lens.

**Near point focusing:**

The image is formed at a near point, i.e. 25 cm for the 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.

**Magnification in near point focusing:**

- 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"` - The magnification can further be written as,

m = `1 - "v"/"f"`(using lens equation)

Substituting for ν with sign convention,

v = - D

m = `1 + "D"/"f"`

This is the magnification for near-point focusing.**Near point focusing**

**Magnification in normal focusing (angular magnification):**

- The magnification for the image is formed at infinity.
- The angular magnification is defined as the ratio angle θ
_{i}, subtended by the image with an aided eye to the angle θ_{0}subtended by the object with unaided eye.

m = `theta_"i"/theta_0`**Normal focusing**

For unaided eye

tan θ_{0} ≈ θ_{0} = `"h"/"D"`

For aided eye

tan θ_{0} ≈ θ_{0} = `"h"/"f"`

The angular magnification is,

m = `theta_"i"/theta_0 = ("h"//"f")/("h"//"D")`

m = `"D"/"f"`

This is the magnification for normal focusing.

Concept: Optical Instruments

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