Please, anyone help me please.
Q: An object is placed 17.8 cm from a first converging lens of focal length 13 cm. A second converging lens with focal length 24 cm is placed 10 cm to the right of the first converging lens. (Take the direction to the right to be positive.)
(a) Find the position q1 of the image formed by the first converging lens.
so, this what I try but, it not right
1/f2=1/q1+1/p1= 1/13-1/17.8=5/234, 234/5= 47cm and it not right answer.
To solve this problem, we can use the lens formula:
1/f = 1/v - 1/u
where:
f = focal length of the lens
v = image distance from the lens (positive for real images, negative for virtual images)
u = object distance from the lens (positive for objects on the same side as the incoming light)
For the first converging lens:
f1 = 13 cm
u1 = -17.8 cm (since the object is placed to the left of the lens, we take it as negative)
Substituting these values into the lens formula:
1/13 = 1/v1 - 1/(-17.8)
1/13 = 1/v1 + 1/17.8
To simplify, we can find a common denominator:
1/13 = (17.8 + v1)/ (v1 * 17.8)
Multiplying both sides by 13v1 * 17.8:
17.8 = (17.8 + v1) * 13
Expanding the equation:
17.8 = 231.4 + 13v1
Rearranging the terms:
13v1 = 17.8 - 231.4
13v1 = -213.6
v1 = -213.6 / 13
v1 ≈ -16.4 cm
Therefore, the position of the image formed by the first converging lens, denoted as q1, is approximately -16.4 cm.
To find the position of the image formed by the first converging lens, we can use the lens formula:
1/f = 1/q - 1/p
Where:
- f is the focal length of the lens
- q is the image position (distance from the lens to the image)
- p is the object position (distance from the lens to the object)
In this case, the focal length of the first converging lens is 13 cm, and the object position (p) is 17.8 cm.
Substituting the values into the lens formula:
1/13 = 1/q1 - 1/17.8
To simplify:
(17.8 - 13) / (13 * 17.8) = 1/q1
(4.8) / (230.8) = 1/q1
0.0208 = 1/q1
q1 = 1 / 0.0208
q1 ≈ 48.08 cm (approximately)
Therefore, the position of the image formed by the first converging lens is approximately 48.08 cm.
Of course it is not right.
Draw a figure. Solve the image location for the first lens, then using that image location as the object location of the second lens, solve for the final image location.
A ray diagram probably will help you keep the numbers realistic.