A person has near point at 100cm.what power of lens is needed to read at a 20cm if he/she uses A)contacts lens B)spectacles having glasses 2.0 cm sepreated from the eyes?

To determine the power of the lens required for a person with a near point of 100 cm to read at 20 cm, we need to consider two scenarios: one for contact lenses and another for spectacles. The power of a lens is calculated using the formula:

Lens Formula and Power Calculation

The lens formula is given by:

1/f = 1/v - 1/u

Where:

• f = focal length of the lens (in meters)
• v = image distance (in meters)
• u = object distance (in meters, taken as negative for real objects)

The power of the lens (P) is related to the focal length by:

P = 1/f (in diopters)

Scenario A: Contact Lenses

For contact lenses, the object distance (u) is the distance from the lens to the object, which is 20 cm or 0.2 m. The near point of the person is 100 cm or 1 m, meaning they can see objects clearly only beyond this distance without assistance.

To find the required focal length:

• u = -0.2 m (the object is at 20 cm)
• v = -1 m (the image must be formed at the near point)

Substituting into the lens formula:

1/f = 1/v - 1/u

1/f = 1/(-1) - 1/(-0.2)

1/f = -1 + 5 = 4

Thus, f = 1/4 = 0.25 m or 25 cm.

Now, calculating the power:

P = 1/f = 1/0.25 = 4 D

So, the power of the contact lens needed is +4 diopters.

Scenario B: Spectacles with Glasses 2.0 cm from the Eyes

In this case, the glasses are positioned 2 cm away from the eyes. Therefore, we need to adjust the image distance accordingly. The effective image distance (v) will be:

v = -1 m + 0.02 m = -0.98 m

Using the same object distance:

• u = -0.2 m
• v = -0.98 m

Now substituting into the lens formula:

1/f = 1/v - 1/u

1/f = 1/(-0.98) - 1/(-0.2)

1/f = -1.0204 + 5 = 3.9796

Thus, f = 1/3.9796 ≈ 0.251 m or 25.1 cm.

Calculating the power:

P = 1/f = 1/0.251 ≈ 3.98 D

Therefore, the power of the spectacles needed is approximately +4 diopters.

Summary of Results

In summary, the power of the lens required for:

• Contact lenses: +4 diopters
• Spectacles (2 cm from the eyes): +4 diopters

Both scenarios yield a similar power requirement, allowing the individual to read comfortably at 20 cm.