Hi! could any help me please, thank you.
1.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.
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and also could you show me how to calculate for this? Thank again
1/28+ 1/v = 1/(-14)
and
Sure! I can help you with that.
To find the position of the image formed by the first converging lens, we can use the lens formula:
1/f = 1/v - 1/u
Where:
f = focal length of the lens
v = distance of the image from the lens (which we need to find)
u = distance of the object from the lens
In this case, the focal length of the first converging lens is 13 cm, and the object is placed 17.8 cm from the lens.
Now, let's calculate the distance of the image (v) using the lens formula:
1/13 = 1/v - 1/17.8
To solve this equation, we can get a common denominator of v * 17.8:
17.8 / (13 * 17.8) = 17.8 * (1/v - 1/17.8)
1/13 = 17.8/v - 1
Next, let's simplify the equation:
1/13 + 1 = 17.8/v
13/13 + 1 = 17.8/v
14/13 = 17.8/v
Cross-multiplying:
14v = 13 * 17.8
Now, divide both sides by 14 to solve for v:
v = (13 * 17.8) / 14
v ≈ 16.57 cm
Therefore, the position of the image formed by the first converging lens is approximately 16.57 cm.
For the equation 1/28 + 1/v = 1/(-14), we can solve for v using similar steps.
1/28 + 1/v = 1/(-14)
To simplify the equation, we can multiply both sides by 28v:
v + 28 = -2v
Combine like terms:
3v = -28
Dividing both sides by 3:
v = -28/3
Therefore, the solution for v is approximately -9.33.