A 15.0cm object is placed 60.0cm from a convex lens which has a focal lenght of 15.0cm use the thin lens equation to find the distance of the image
(60)1/15=1/60+1/60(1/15)=1-1+1/d
I don't understand your work.
1/di+1/d0=1/f
1/di+1/60=1/15
1/di=3/60
di=20cm
check that.
Well, well, well, let's solve this equation with a touch of humor, shall we?
So, we have our thin lens equation: (60 cm)^(-1) = (15 cm)^(-1) + (60 cm)^(-1)(15 cm)^(-1)
Now, let's combine those little fractions using a common denominator to make our lives easier. And the denominator is... *drumroll*... 900 cm!
So, now we have: (60 cm)^(-1) = (900 cm)/(15 cm) + (900 cm)/(60 cm)(15 cm)
Simplifying, we get: (60 cm)^(-1) = 60/900 + 900/900
After simplifying even more, we get: (60 cm)^(-1) = 1/15 + 1
And lo and behold, the equation transforms into: (60 cm)^(-1) = 2/15
Now, all we need to do is take the reciprocal of both sides, and we find that: (60 cm) = 15/2
Finally, dividing by the original object distance of 15.0 cm, we get: (60 cm) / (15 cm) = 4
Ta-da! The distance of the image is 4 times the object distance.
I hope you enjoyed this humorous mathematical journey!
To find the distance of the image using the thin lens equation, which is given by:
1/f = 1/di - 1/do
where f is the focal length of the lens, di is the distance of the image, and do is the distance of the object.
Given:
focal length (f) = 15.0 cm
distance of the object (do) = 60.0 cm
Substituting these values into the thin lens equation, we get:
1/15 = 1/di - 1/60
To solve for the distance of the image (di), we need to rearrange the equation:
1/di = 1/15 + 1/60
Let's simplify this equation step by step:
1/di = (4/60) + (1/60) = 5/60
To isolate di, we take the reciprocal of both sides:
di = 60/5 = 12.0 cm
Therefore, the distance of the image is 12.0 cm.
To find the distance of the image using the thin lens equation, we can follow these steps:
1. Convert all distances to meters: In this case, the object distance is 60.0 cm = 0.60 m, while the focal length of the lens is also 15.0 cm = 0.15 m.
2. Substitute the values into the thin lens equation: The thin lens equation is given by:
1/f = 1/di - 1/do,
where
- f represents the focal length of the lens,
- di represents the distance of the image, and
- do represents the distance of the object.
Plugging in the known values:
1/0.15 = 1/di - 1/0.60.
3. Simplify the equation: We need to find the term 1/di. To do this, we can multiply both sides of the equation by 0.60. This yields:
0.60/0.15 = 0.60/di - 0.60/0.60.
Simplifying the right side:
4 = 0.60/di - 1.
4. Rearrange the equation to isolate 1/di: Add 1 to both sides of the equation:
5 = 0.60/di.
Divide both sides of the equation by 5:
1/di = 0.60/5.
Simplifying the right side:
1/di = 0.12.
5. Take the reciprocal of both sides: Taking the reciprocal of both sides of the equation gives us:
di = 1/(0.12).
6. Calculate the distance of the image: Evaluating the reciprocal gives us:
di ≈ 8.33 m.
Therefore, the distance of the image is approximately 8.33 meters.