here is my problem:
a concave mirror forms a real image at 17.0 cm from the mirror surface along the principal axis. if the corresponding object is at a distance of 36.0 cm, what is the mirror's focal length?
here's my work: 1/f = 1/v + 1/u
where f=focal length=?
u= -36 cm (object distance)
v= -17 cm (image distance)
1/f = -1/17 - 1/36
f= -11/54 cm
is this the correct way to do this? is there any other way that is better? is the answer correct? thanks
a tutor told me the u and v and the computed f should all be positive...
should ijust change the signs..or do i have to solve again ? will the anser remain the same number?
I agree on the positive signs.
17*36/(17+36)=
(17 * 36) / (17 + 36) = 11.5 cm
Your approach to using the mirror formula, 1/f = 1/v + 1/u, is correct. However, your tutor is correct as well - the object and image distances should be positive in this case because the concave mirror is forming a real image.
To clarify, when using the mirror formula, distances should be defined by a positive value when the object is on the same side of the mirror as the incoming light (the left side in this case), and the image distance should be positive when the image is on the opposite side of the mirror from the incoming light.
Since you have the object distance as -36 cm and the image distance as -17 cm, you should change the signs to positive.
Let's re-evaluate the formula:
1/f = 1/v + 1/u
1/f = 1/17 + 1/36
1/f = (36 + 17) /(17 * 36)
1/f = 53/612
f = 612/53 cm (approximately 11.55 cm)
Therefore, the focal length of the concave mirror is approximately 11.55 cm.
Your approach to solving the problem using the lens formula is correct. However, there seems to be a sign error in your calculation. Let's go through the steps again:
Given:
Object distance (u) = -36.0 cm
Image distance (v) = -17.0 cm
Focal length (f) = ?
Using the lens formula:
1/f = 1/v + 1/u
Substituting the given values:
1/f = 1/(-17.0) + 1/(-36.0)
1/f = -0.0588 - 0.0278
1/f = -0.0866
Now, to find the value of f, take the reciprocal of both sides:
f = -11.54 cm (approx.)
The correct answer for the focal length is approximately -11.54 cm, not -11/54 cm.
As for the sign convention, it is important to be consistent. In the lens formula, the sign convention commonly used is as follows:
- Distances measured towards the mirror are positive (u > 0, v > 0, and f > 0 for a concave mirror).
- Distances measured away from the mirror are negative (u < 0, v < 0, and f < 0 for a concave mirror).
In this case, since both the object and image distances are given as negative values, you can keep the negative signs for both u and v. However, the resulting focal length should be positive according to the sign convention.
Therefore, in your solution, simply change the sign of the focal length:
f = 11.54 cm
So, the correct answer for the focal length of the concave mirror is approximately +11.54 cm.