An object is to be seen through a microscope of focal length 12cm.where should be the object so as to produce maximum angular magnification ?The least distance for clear vision is 25cm

To determine where the object should be placed to achieve maximum angular magnification when viewed through a microscope with a focal length of 12 cm, we need to consider a few optical principles. The angular magnification of a microscope is influenced by the position of the object relative to the focal point of the lens and the least distance of distinct vision, which is typically around 25 cm for a human eye.

Understanding Angular Magnification

Angular magnification (M) can be expressed as the ratio of the angle subtended by the image at the eye to the angle subtended by the object at the same eye. For a simple microscope, the formula can be simplified to:

• M = (D / f) + 1

Where:

• D is the least distance of distinct vision (25 cm).
• f is the focal length of the lens (12 cm).

Finding the Optimal Object Distance

To maximize angular magnification, we need to place the object at the focal point of the lens. However, to achieve the best results, we also need to consider the distance of the object from the lens. The object distance (u) can be calculated using the lens formula:

• 1/f = 1/v - 1/u

Where:

• v is the image distance.
• u is the object distance.

Calculating the Image Distance

For maximum angular magnification, we want the image to be formed at the least distance of distinct vision (D = 25 cm). Rearranging the lens formula gives us:

• 1/u = 1/v + 1/f

Substituting the values:

• v = -25 cm (the negative sign indicates that the image is virtual and on the same side as the object).
• f = 12 cm.

Now, substituting these into the lens formula:

• 1/u = 1/(-25) + 1/12
• 1/u = -0.04 + 0.0833
• 1/u = 0.0433

Calculating u gives:

• u ≈ 23.1 cm.

Conclusion on Object Placement

To achieve maximum angular magnification with a microscope of focal length 12 cm, the object should be placed approximately 23.1 cm from the lens. This positioning allows the image to be formed at the least distance of distinct vision (25 cm), optimizing the viewing experience through the microscope.