Convex mirror find object distance

In summary, when an object is placed in front of a convex mirror with a 45.6-cm radius of curvature, a virtual image half the size of the object is formed. Using the equations 1/f=1/d0+1/di and hi/h0=-di/d0, the distance of the object from the mirror is calculated to be 68.4 cm. However, the negative sign in the equation for di=-1/2d0 may not be necessary as the virtual image is erect.
  • #1
xamy
27
0

Homework Statement


An object is placed in front of a convex mirror with a 45.6-cm radius of curvature. A virtual image half the size of the object is formed. At what distance is the object from the mirror?

Homework Equations


1/f=1/d0+1/di
hi/h0=-di/d0

The Attempt at a Solution


hi=-1/2h0
f=45.6/2=22.8

di=-1/2d0

1/22.8=1/d0-2/d0
d0=-22.8

This is my solution but this is nor correct...anyone please tell me the mistake. thanks!
 
Physics news on Phys.org
  • #2
xamy said:
di=-1/2d0
Firstly please use brackets, it looks like it may be ##d_i=\frac{-1}{2d_o}##or ##d_i=\frac{-1}{2}d_o##
and i don't see the need for the -ve sign in the above equation(logically).
Also because when you substitute the ##h_i## you should negate it as it is inverted, so there shouldn't be a -ve sign for your above equation
 
  • #3
Suraj M said:
Firstly please use brackets, it looks like it may be ##d_i=\frac{-1}{2d_o}##or ##d_i=\frac{-1}{2}d_o##
and i don't see the need for the -ve sign in the above equation(logically).
Also because when you substitute the ##h_i## you should negate it as it is inverted, so there shouldn't be a -ve sign for your above equation

ok so after editing the ans becomes
1/22.8=1/d0+2/d0
d0=68.4
 
  • #4
I'm sorry i correct myself, i thought it was a concave mirror, so you shouldn't negate ##h_i## as it is erect.
you were right. The answer you have obtained, looks to be right. Why do you feel it is wrong?
 

1. How does a convex mirror help in finding the object distance?

A convex mirror is a spherical mirror with a reflective surface that curves outwards. When an object is placed in front of a convex mirror, the light rays from the object are reflected in such a way that they diverge. By tracing these diverging rays back to the mirror, we can determine the apparent size and location of the virtual image formed, which can then be used to calculate the object distance.

2. What is the formula for calculating the object distance in a convex mirror?

The formula for calculating the object distance in a convex mirror is: do = -r2 / (4f), where do is the object distance, r is the radius of curvature of the mirror, and f is the focal length of the mirror.

3. Does the object distance affect the size of the image formed in a convex mirror?

Yes, the object distance does affect the size of the image formed in a convex mirror. As the object distance increases, the size of the image decreases and vice versa. This is because the image formed by a convex mirror is always virtual, upright, and smaller than the actual object.

4. Can a convex mirror be used to form a real image?

No, a convex mirror cannot form a real image. This is because the reflected rays never converge to a point, but always diverge from a virtual image behind the mirror. The image formed by a convex mirror is always virtual, upright, and smaller than the actual object.

5. How accurate is the object distance calculation in a convex mirror?

The object distance calculation in a convex mirror is reasonably accurate for small objects and small distances from the mirror. However, for larger distances, the calculation may become less accurate due to the simplifying assumptions made in the formula.

Similar threads

  • Introductory Physics Homework Help
Replies
5
Views
461
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
918
  • Introductory Physics Homework Help
Replies
3
Views
4K
  • Introductory Physics Homework Help
Replies
7
Views
913
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
1K
Back
Top