when two lenses of focal length +10cm and -5cm are placed in contact then find the net power ?
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To find the net power when two lenses are placed in contact, you can use the formula:
P_net = P_1 + P_2 - P_1 * P_2 / d
Where:
P_net is the net power,
P_1 is the power of the first lens,
P_2 is the power of the second lens, and
d is the distance between the lenses.
Given:
Focal length of the first lens, f_1 = +10 cm
Power of the first lens, P_1 = 1/f_1 = 1/10 cm^(-1)
Focal length of the second lens, f_2 = -5 cm
Power of the second lens, P_2 = 1/f_2 = 1/(-5) cm^(-1)
Since the two lenses are placed in contact, the distance between them, d = 0 cm
Let's substitute the given values into the formula:
P_net = P_1 + P_2 - P_1 * P_2 / d
= 1/10 cm^(-1) + 1/(-5) cm^(-1) - (1/10 cm^(-1)) * (1/(-5) cm^(-1)) / 0 cm
However, dividing by zero is undefined, so we cannot evaluate the expression. In this case, the net power cannot be determined because the lenses are touching.
To find the net power of two lenses placed in contact, we need to use the formula for combining the power of lenses in contact:
1/F = 1/f1 + 1/f2
Where F is the net power, f1 is the focal length of the first lens, and f2 is the focal length of the second lens.
Given that the focal length of the first lens (f1) is +10cm and the focal length of the second lens (f2) is -5cm, we can substitute these values into the formula:
1/F = 1/10 + 1/(-5)
To simplify the equation, we find the common denominator:
1/F = (-1 + 2)/10 = 1/10
Therefore, the net power (F) is +10 cm or 10 diopters.
So, when two lenses with focal lengths of +10 cm and -5 cm are placed in contact, the net power is +10 diopters.