The image of your nose is located inside the spherical salad bowl.
To determine the exact location of the image, we can use the formula for the thin lens equation, which is given by:
1/f = 1/v - 1/u
Where:
- f is the focal length of the lens
- v is the distance of the image from the lens
- u is the distance of the object from the lens
In this case, the salad bowl acts as a concave mirror, which means its focal length (f) is equal to half of the radius of curvature (R). Given that the radius of curvature is 40 cm, the focal length of the salad bowl is 20 cm.
Since the object (your nose) is placed at a distance of 50 cm in front of the salad bowl, the object distance (u) is equal to -50 cm (negative because it is on the same side as the observer).
Plugging these values into the thin lens equation, we have:
1/20 = 1/v - 1/-50
Simplifying this equation, we find:
1/v = 1/20 + 1/50
1/v = (5 + 2)/100
1/v = 7/100
Cross-multiplying, we get:
v = 100/7
So, the image of your nose is located approximately 14.29 cm from the salad bowl's surface.
Since the image is located inside the salad bowl, it will appear smaller than the actual nose. The height of the image can be determined using the magnification equation:
magnification (m) = -v/u
Plugging in the values:
m = - (100/7) / (-50)
m = 2/7
The magnification is positive, indicating that the image is upright.
To find the height of the image, we can use the formula:
image height / object height = magnification
Plugging in the values:
image height / 5.0 = 2/7
Cross-multiplying:
image height = (2/7) * 5.0
image height = 1.43 cm
Therefore, the image of your 5.0 cm tall nose is located approximately 14.29 cm from the surface of the salad bowl and has a height of 1.43 cm.