Physics lenses. Please help, my math is wrong and I need second opinion.?
Consider three lenses with focal lengths of 25.9 cm, -15.8 cm, and 10.0 cm positioned on the x axis at x1 = 0 m, x2 = 0.412 m, and x3 = 0.514 m, respectively. An object is at d = -121 cm.
Find the location of the final image produced by this lens system. x=___m
Find the magnification of the final image produced by this lens system. m =____
work is here
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The first lens
do = 121, f1 = 25.9
1/di + 1/do =1/f1,
di = 32.9 cm
It is the image for the second lens. It is 41.2 – 32.9 = 8.25 cm far from the second lens.
do=8.25, f2 =15.8
1/do -1/di =-1/f2.
di =13.2 cm.
Again this would work as image for the 3rd lens.
It is 51.2 -13.2 = 28cm from the origin of the coordinate system and distance 51.4 – 28 = 23.4 cm from the 3rd lens.
do =23.4, f3 = 10
1/di + 1/do = 1/f3
di =17.5.
The final image is 17.5 + 51.4 =68.9 cm from the origin of the coordinate system.
M = di/do, and M =M1•M2 •M3=
=(32.9/121) •(13.2/8.25) •(17.5/23.4) =0.325.
If you know the answer, show it. please
How much work is required to lift a 5.1-kg concrete block to a height of 3.6 m
To find the location of the final image produced by this lens system, you can use the lens formula:
1/f = 1/v - 1/u
where f is the focal length of the lens, v is the image distance from the lens, and u is the object distance from the lens.
Given the object distance (u) as d = -121 cm, we need to find the image distance (v) for each lens and combine them to get the final image distance.
For the first lens (focal length = 25.9 cm) at x1 = 0 m:
1/25.9 = 1/v1 - 1/-121
Now, rearrange the equation to solve for v1:
1/v1 = 1/25.9 + 1/121
v1 = 1 / (1/25.9 + 1/121)
Calculate v1 using the above equation.
For the second lens (focal length = -15.8 cm) at x2 = 0.412 m:
1/-15.8 = 1/v2 - 1/v1
Now, rearrange the equation to solve for v2:
1/v2 = 1/-15.8 + 1/v1
v2 = 1 / (1/-15.8 + 1/v1)
Substitute the value of v1 calculated earlier to find v2.
Finally, for the third lens (focal length = 10.0 cm) at x3 = 0.514 m:
1/10.0 = 1/v3 - 1/v2
Now, rearrange the equation to solve for v3:
1/v3 = 1/10.0 + 1/v2
v3 = 1 / (1/10.0 + 1/v2)
Substitute the value of v2 calculated earlier to find v3.
The location of the final image produced by this lens system is the image distance of the third lens, v3.
To find the magnification (m) of the final image produced by this lens system, you can use the magnification formula:
m = -v3 / u
Substitute the values of v3 and u (object distance) to find the magnification.
By following these steps and calculations, you should be able to get the correct location of the final image and its magnification.