Exploring Image Formation in a Spherical Salad Bowl
Where is the image of your 5.0-cm-tall nose located in a spherical salad bowl?
Final answer:
The image of your nose is located approximately 39.41 cm away from the salad bowl.
Explanation:
To determine the location of the image of your nose, we can use the mirror equation: 1/do + 1/di = 2/R, where do is the object distance, di is the image distance, and R is the radius of curvature of the mirror.
In this case, the object distance is 70 cm and the radius of curvature is 48 cm. By substituting these values into the equation, we can solve for the image distance:
1/70 + 1/di = 2/48
After rearranging the equation and solving for di, we find that the image distance is approximately 39.41 cm.
Understanding the Image Location
Image Distance Calculation: The image distance is calculated using the mirror equation, taking into account the object distance and the radius of curvature of the mirror.
Numerical Calculation: Substituting the values of the object distance and radius of curvature into the mirror equation allows us to determine the image distance as approximately 39.41 cm.
What is the size of the image of your nose in the spherical salad bowl?
Final answer:
The image of your nose has a magnification of -0.5629.
Explanation:
The size of the image can be determined using the magnification formula: m = -di/do, where m is the magnification, di is the image distance, and do is the object distance.
In this case, di is 39.41 cm and do is 70 cm. By substituting these values into the formula, we can solve for the magnification:
m = -39.41/70 ≈ -0.5629
Unraveling the Image Size
Magnification Calculation: The magnification of the image is determined by relating the image distance to the object distance in the magnification formula.
Interpreting the Magnification: The negative sign in the magnification value indicates that the image is inverted relative to the object. The magnification of -0.5629 signifies that the image of your nose is reduced in size and inverted.