the two lenses in contact are 45 cm away from the object and the distance of the object from the image is 110 cm. if one of the two lenses in contact has a focal length of 15cm, what is the focal length of the second lens? thanks :)
To find the focal length of the second lens, we can use the lens formula. The lens formula states:
1/f = 1/v - 1/u
Where:
f = focal length of the lens
v = image distance from the lens (positive if on the opposite side of the object)
u = object distance from the lens (positive if on the same side as the object)
According to the information given, the object distance, u, is 45 cm. And the image distance, v, is 110 cm.
Since the two lenses are in contact, their power add up. The power of a lens is defined as P = 1/f, where P is the power of the lens and f is the focal length.
Let's denote the focal length of the second lens as f2. The total power of the two lenses in contact is the sum of their individual powers:
Power of lens 1 + Power of lens 2 = Total Power
(1/f1) + (1/f2) = Total Power
Now, we can substitute the values and simplify the equation:
(1/15) + (1/f2) = Total Power
To find the Total Power, we need to convert the object and image distances into meters, since the focal length values are often given in meters. So, 45 cm becomes 0.45 m, and 110 cm becomes 1.1 m.
Let's calculate the Total Power:
Total Power = 1/0.45 - 1/1.1
Now, we find the value of Total Power. Once we have this value, we can solve for 1/f2:
Total Power = 1/f2
Finally, we can determine the focal length of the second lens, f2, by taking the reciprocal of the Total Power:
f2 = 1 / Total Power
By substituting the values and performing the calculations, you'll be able to find the focal length of the second lens.