Ray Optics Q2: Find Focal Length of Mirror

In summary, an object with a height of 2.0 cm is placed in front of a mirror, creating an upright image with a height of 1.0 cm behind the mirror at a distance of 165 cm from the object. The focal length of the mirror cannot be determined without more information. The attempt at a solution of 37 cm was incorrect.
  • #1
sphouxay
18
0

Homework Statement


A 2.0--cm tall object is placed in front of a mirror. A 1.0--cm tall upright image is formed behind the mirror, 165 cm from the object.

What is the focal length of the mirror?

Homework Equations





The Attempt at a Solution


I tried 37 cm, it was incorrect
 
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  • #2
sphouxay said:

Homework Statement


A 2.0--cm tall object is placed in front of a mirror. A 1.0--cm tall upright image is formed behind the mirror, 165 cm from the object.

What is the focal length of the mirror?

Homework Equations





The Attempt at a Solution


I tried 37 cm, it was incorrect

Why did you try 37? What equations are you using?
 
  • #3
.

The correct focal length of the mirror can be calculated using the mirror equation:

1/f = 1/do + 1/di

Where f is the focal length, do is the object distance, and di is the image distance.

In this case, do = -165 cm (since the object is placed in front of the mirror) and di = +1 cm (since the image is formed behind the mirror).

Substituting these values into the equation:

1/f = 1/-165 + 1/1

1/f = -1/165 + 1

1/f = 164/165

f = 165/164 cm

Therefore, the focal length of the mirror is approximately 1.006 cm. It is important to note that the focal length of a mirror is always positive and the negative sign in the object distance is used to indicate that the object is located in front of the mirror.
 

Related to Ray Optics Q2: Find Focal Length of Mirror

1. What is ray optics?

Ray optics is a branch of optics that studies the behavior of light as it travels in a straight line, also known as a ray. It is used to understand the properties and characteristics of light and how it interacts with different materials, such as mirrors and lenses.

2. How do you find the focal length of a mirror?

To find the focal length of a mirror, you can use the formula: f = r/2, where f is the focal length and r is the radius of curvature. This formula applies to both concave and convex mirrors. You can also find the focal length experimentally by measuring the distance between the mirror and the point where the image of an object is formed.

3. What is the difference between a concave and a convex mirror?

A concave mirror curves inward, causing light rays that strike it to converge at a point, known as the focal point. This type of mirror is used to magnify objects and form real images. A convex mirror, on the other hand, curves outward and causes light rays to diverge, making objects appear smaller. This type of mirror is commonly used in rear-view mirrors and security mirrors.

4. Can the focal length of a mirror be changed?

Yes, the focal length of a mirror can be changed by changing the curvature of the mirror's surface. For example, a concave mirror can have a shorter or longer focal length depending on how much it is curved. Additionally, the focal length can be changed by moving the object or the mirror itself.

5. How is the focal length of a mirror related to its power?

The power of a mirror is inversely proportional to its focal length. This means that a mirror with a shorter focal length will have more power, while a mirror with a longer focal length will have less power. The unit of measurement for the power of a mirror is diopters (D).

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