A converging lens forms a virtual image 2.61
times the size of the objecT. The object distance is 11cm. Find the distance of the focal point from the center of the lens.
To find the distance of the focal point from the center of the lens, 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,
u is the object distance from the lens.
In this case, you are given:
v = -2.61u (since the image formed is virtual and magnified, its distance is negative)
u = 11 cm
Substituting these values into the lens formula:
1/f = 1/(-2.61u) - 1/u
Simplifying further:
1/f = (-1/2.61u) - (1/u)
1/f = (-1 - 2.61) / (2.61u)
1/f = -3.61 / (2.61u)
To find f, we need the equation in terms of f:
1/f = -3.61 / (2.61u)
Now, we can substitute the given u value:
1/f = -3.61 / (2.61 * 11)
Calculating the right-hand side of the equation:
1/f = -3.61 / 28.71
1/f ≈ -0.1256
Taking the reciprocal:
f ≈ -1 / (-0.1256)
f ≈ 7.968 cm
Therefore, the distance of the focal point from the center of the lens is approximately 7.968 cm.
To find the distance of the focal point from the center of the lens, we can use the magnification formula:
magnification = -image distance / object distance
where the magnification is given as 2.61 and the object distance is 11 cm. Since the image formed by a converging lens is virtual and on the same side of the lens as the object, the image distance is negative.
Substituting the given values, we have:
2.61 = -image distance / 11 cm
To find the image distance, we can rearrange the formula:
image distance = -2.61 * 11 cm
image distance ≈ -28.71 cm
Now, we can use the lens formula to find the focal length:
1 / focal length = 1 / object distance + 1 / image distance
Since the object distance is positive and the image distance is negative, the lens formula becomes:
1 / focal length = 1 / 11 cm + (-1 / 28.71 cm)
1 / focal length = 0.0909 cm^(-1) - 0.0348 cm^(-1)
1 / focal length ≈ 0.0561 cm^(-1)
Now, we can find the focal length:
focal length ≈ 1 / (0.0561 cm^(-1))
focal length ≈ 17.81 cm
Therefore, the distance of the focal point from the center of the converging lens is approximately 17.81 cm.