To solve this problem, we'll use the mirror equation and the magnification formula for convex mirrors.
(a) Location of the image:
We'll use the mirror equation:
1/f = 1/do + 1/di
where f is the focal length of the mirror, do is the object distance, and di is the image distance.
Since the mirror is convex, the focal length (f) is positive, given by:
f = R/2
where R is the radius of curvature of the mirror.
Substituting the values R = 17 cm and do = 25 cm into the mirror equation, we have:
1/(17/2) = 1/25 + 1/di
Solving this equation, we can find the value of di, which represents the location of the image.
(b) Height of the image:
We'll use the magnification formula:
m = -di/do
where m is the magnification, di is the image distance, and do is the object distance.
Substituting the values do = 25 cm and di (from part a) into the magnification formula, we can calculate the value of m.
Next, let's move on to the second scenario:
(c) Location of the image:
Again, we'll use the mirror equation with the new value of do = 5.1 cm:
1/(17/2) = 1/5.1 + 1/di
Solving this equation, we can find the value of di, representing the location of the image.
(d) Height of the image:
Using the magnification formula, m = -di/do, with the new values do = 5.1 cm and di (from part c), we can calculate the value of m.
(e) Ratio of image height:
The ratio of image heights for the two scenarios can be calculated by dividing the height of the image (from part d) when do = 5.1 cm by the height of the image when do = 25 cm.
By following these steps, you should be able to find the location and height of the image for each scenario, as well as the ratio of the image heights.