Open Question
You hold a spherical salad bowl 60 cm in front of your face with the bottom of the bowl facing you. The bowl is made of polished metal with a 35-cm radius of curvature. (a) Where is the of your 5.0-cm-tall nose located?
33. Geometric Optics
Mirror Equation
Struggling with Physics?
Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
You want to produce a mirror that can produce an upright image that would be twice as tall as the object when placed 5 cm in front of it. What shape should this mirror be? What radius of curvature should the mirror have?
A
concave; 20cm
B
convex; 20cm
C
concave; 10cm
D
convex; 10 cm
E
It is not possible
Verified step by step guidance1
Identify the type of image described: An upright image that is twice as tall as the object indicates a magnification of +2.
Recall the magnification formula for mirrors: \( m = \frac{-d_i}{d_o} \), where \( m \) is the magnification, \( d_i \) is the image distance, and \( d_o \) is the object distance. Since the image is upright, the magnification is positive.
Substitute the given values into the magnification formula: \( 2 = \frac{-d_i}{5} \). Solve for \( d_i \) to find the image distance.
Use the mirror equation: \( \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \), where \( f \) is the focal length. Substitute \( d_o = 5 \) cm and the calculated \( d_i \) to find \( f \).
Determine the radius of curvature \( R \) using the relationship \( R = 2f \). Identify the mirror type based on the sign of \( f \) (positive for concave, negative for convex) and calculate \( R \).
Related Videos
Related Practice
Mirror Equation practice set
Problem sets built by lead tutorsExpert video explanations