A lamp is 5.0 m from a wall. Find the focal length of the concave mirror which will form a four times magnified image of the wall.
- print Print
- list Cite
Expert Answers
calendarEducator since 2013
write455 answers
starTop subjects are Science, Math, and History
See the figure below for the ray diagram.
The equation that relates the position of the object, image and focal distance for a spherical mirror is
`1/(x1) +1/(x2) =1/f`
using the following conventions
x1 (the position of the object) is positive if the object is to the left of the mirror
x2 (the position of the image) is positive if the image is to the left of the mirror
f (focal distance) is positive for concave mirrors
By definition the magnification is
`M =-(y2)/(y1) =-(x2)/(x1)`
With the data in text one has
`x2 =-4*x1`
`1/(x1) -1/(4*x1) =1/f`
`3/(4*x1) =1/f`
`f = (4*x1)/3 =(4*5)/3 =6.67 m`
Because the magnification is positive the image is behind the mirror which means it is virtual.
Related Questions
- If you are given concave mirrors with focal length 10 cm, 15 cm and 20 cm, which one is most...
- 1 Educator Answer
- A concave mirror magnifies an object placed 30.0cm from the mirror by a factor of +3.0. Calculate...
- 1 Educator Answer
- A concave mirror magnifies an object placed 30.0cm from the mirror by a factor of +3.0. Calculate...
- 1 Educator Answer
- A small plane mirror is placed 21 cm in front of a concave mirror of focal length 21 cm. An...
- 1 Educator Answer
- A convex mirror has a focal length of −15 cm.What is the object distance if the image distance...
- 2 Educator Answers
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.