Optical instrument magnifying glass – problems and solutions

1. A 2 mm high object is placed 10 cm from a magnifying glass. Near point N = 25 cm. Determine the angular magnification and image height.

Known :

Object height (ho) = 2 mm

Near point (N) = 25 cm

Object distance (do) = 10 cm

Wanted : Angular magnification (M) and image height (hi)

Solution :

M = N / s

M = 25 cm / 10 cm

M = 2.5

The image height = 2.5 x 2 mm = 5 mm.

2. A 25 cm focal length lens is used as magnifying glass. Determine (a) angular magnification when the eye is focused at its near point N = 25 cm (b) angular magnification when the eye is relaxed.

Known :

Near point (N) = 25 cm

The focal length of a magnifying glass (f) = 25 cm

The plus sign indicates that the lens is a converging lens.

Solution :

(a) angular magnification when the eye is focused at its near point N = 25 cm

M = (N/f) + 1

M = (25 cm / 25 cm) + 1

M = 1 + 1

M = 2 X

If the object height is 1 cm, the image height is 2 x 1 cm = 2 cm.

(b) angular magnification when the eye is relaxed

M = N / f

M = (25 cm / 25 cm)

M = 1 X

If the object height is 1 cm, the image height is 1 x 1 cm = 1 cm.

3. A 1 cm high object is placed in front of a 10 cm focal length lens. Determine (a) the image height when the eye is focused at its near point N = 25 cm (b) The image height when the eye is relaxed.

Known :

The object height (ho) = 1 cm

The focal length (f) = 10 cm

Near point (N) = 25 cm

Solution :

(a) The image height when the eye is focused at its near point N = 25 cm

M = (N/f) + 1

M = (25 cm / 10 cm) + 1

M = 2.5 + 1

M = 3.5 X

If the object height is 1 cm, the image height is 3.5 x 1 cm = 3.5 cm.

(b) The image height when the eye is relaxed.

M = N/f

M = 25 cm / 10 cm

M = 2.5 X

If the object height is 1 cm, the image height is 2.5 x 1 cm = 2.5 cm.

4. The angular magnification when the eye is relaxed = 5X. If near point = 25 cm, what is the focal length of the magnifying glass ?

Known :

Object height (ho) = 2 mm

Angular magnification (M) = 5X

Near point (N) = 25 cm

Wanted: The focal length

Solution :

The formula of the angular magnification when the eye is relaxed :

M = N/f

5 = 25 cm / f

f = 25 cm / 5

f = 5 cm

The focal length of the magnifying glass = 5 cm.

5. An object is seen by someone with a magnifying glass with the focal length is 15 cm. If the near point of the person’s eyes = 30 cm, then determine the overall magnification of the magnifying glass.

Known :

The near point of the normal eye (N) = 30 cm

The focal length of the magnifying glass (f) = 15 cm (plus sign because the glass is convergent)

Wanted : the maximum magnification

Solution :

The maximum magnification occurs when the accommodation of eye is maximum. The angular magnification of the magnifying glass occurs when the accommodation of eye is maximum :

M = (N/f) + 1

M = (30 cm / 15 cm) + 1

M = 2 + 1

M = 3 times

6. A magnifying glass with the optical power 20 diopters used by a person with the normal eyes 25 cm. If the accommodation is minimum, determine the minimum magnification.

Known :

Near point of the normal eye (N) = 25 cm

Power of the magnifying glass (P) = 20 diopters

Wanted: The minimum magnification

Solution :

The focal length of the magnifying glass :

P = 1/f

20 = 1/f

f = 1/20

f = 0.05 meters

f = 5 cm

The angular magnification when the accommodation is minimum :

M = N / f

M = (25 cm / 5 cm)

M = 5 times

  1. Concave mirror problems and solutions
  2. Convex mirror problems and solutions
  3. Diverging lens problems and solutions
  4. Converging lens problems and solutions
  5. Optical instrument human eye problems and solutions
  6. Optical instrument contact lenses problems and solutions
  7. Optical instrument eyeglasses
  8. Optical instrument magnifying glass problems and solutions
  9. Optical instrument microscope – problems and solutions
  10. Optical instrument telescopes problems and solutions
Read :  Wheels connected by belts - problems and solutions