Mirror Formula §

Introduction §

The mirror formula is a fundamental concept in optics, particularly when studying concave and convex mirrors. This formula relates the object distance ($u$), the image distance ($v$), and the focal length ($f$) of a mirror. Understanding this formula is crucial for predicting how mirrors affect the path of light rays, and it has practical applications in various fields, from astronomy to everyday objects like shaving mirrors.

The Mirror Formula §

The mirror formula is given by:

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

Where:

• $f$ is the focal length of the mirror.
• $v$ is the distance from the mirror to the image.
• $u$ is the distance from the mirror to the object.

Sign Convention §

In the mirror formula, it’s essential to follow the sign convention:

• Distances measured in the direction of the incident light (towards the mirror) are positive.
• Distances measured against the direction of the incident light (away from the mirror) are negative.
• For a concave mirror, the focal length ($f$) is negative, and for a convex mirror, it is positive.

Applications §

• Astronomy: Telescopes use mirrors to form images of distant celestial bodies.
• Medical Devices: Devices like endoscopes use mirrors for internal imaging.
• Everyday Use: From vehicle rear-view mirrors to makeup mirrors.

Historical Context §

The development of the mirror formula can be traced back to the works of ancient scholars like Euclid and Alhazen. Their foundational work in optics laid the groundwork for later scientists like Isaac Newton and Johannes Kepler, who further developed our understanding of optical phenomena.

Examples §

1. Concave Mirror: When an object is placed beyond the focal length of a concave mirror, a real, inverted image is formed.
2. Convex Mirror: A convex mirror always forms a virtual, upright, and diminished image, regardless of the object’s position.

Test Questions §

1. STARTI [Basic] Question: What is the mirror formula? Back: The mirror formula is $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$, where $f$ is the focal length, $v$ is the image distance, and $u$ is the object distance. ENDI
2. STARTI [Basic] Question: In the mirror formula, if an object is placed 30 cm in front of a concave mirror with a focal length of 15 cm, where is the image formed? Back: Using the formula $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$, and putting $f=-15$ cm (since it’s a concave mirror), $u=-30$ cm, we find that $v=-30$ cm, which means the image is formed at 30 cm in front of the mirror. ENDI
3. STARTI [Basic] Question: Why is the focal length of a convex mirror taken as positive? Back: According to the mirror sign convention, distances measured in the direction of incident light (towards the mirror) are positive. Since the focal point of a convex mirror is virtual and appears to be in the direction of the incident light, its focal length is considered positive. ENDI

Optics | Concave and Convex Mirrors | Light and Reflection