Define power of a lens. Find the focal length of a lens which should be placed incontact with a lens of focal length 10cm so that the power of the combination is 5Dioptre

The power of a lens is defined as the reciprocal of its focal length. It is measured in dioptres (D). The formula to calculate the power (P) of a lens is:

P = 1/f

where f is the focal length of the lens in meters.

Given in the problem, we have a lens with a focal length of 10 cm, which is 0.1 m. The power of this lens (P1) can be calculated as:

P1 = 1/0.1 = 10 D

We also know that the power of the combination of this lens with another lens is 5 D. When lenses are placed in contact, their powers are additive. Therefore, the power of the second lens (P2) can be calculated as:

P2 = P (total) - P1 P2 = 5 D - 10 D = -5 D

The negative sign indicates that the second lens is a diverging lens. The focal length of this lens (f2) can be calculated as:

f2 = 1/P2 f2 = 1/-5 = -0.2 m

So, the focal length of the lens which should be placed in contact with the lens of focal length 10 cm so that the power of the combination is 5 D is -0.2 m or -20 cm. The negative sign indicates that the lens is a diverging lens.