Mirror and Lens Formula

The mirror and lens formulae are equations used to relate the focal length (f), object distance (u), and image distance (v) for mirrors and lenses. Let’s discuss both formulas below:

Mirrors Formula

The mirror formula establishes a relation between the object distance (u), image distance (v) and focal length of a spherical mirror. Mirror formula is given as,

Where,

• v is the distance of image from the pole (O) of the mirror.
• u is the distance of object from the pole (O) of the mirror.
• f is the focal length of the spherical mirror.

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Lens Formula

The lens formula gives a relation between the object distance (u), image distance (v) and focal length of a given lens. Lens formula is given as,

Where,

• v is the distance of image from the center (O) of the lens.
• u is the distance of object from the center (O) of the lens.
• f is the focal length of the lens.

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Sign Convention for Mirror and Lens

To use the mirror and lens formula correctly, we need to follow standard sign conventions. These are some rules which are applied while solving optical numerical:

• All the distances are measured from the pole and optical center (O) of the mirror and lens respectively.
• The distances measured along the direction of incident rays are positive. While the distances measured opposite to the direction of incident rays are considered negative.
• The object is always placed on the left side of mirror or lens, so the value of distance of object from the optical center (u) is always negative.
• If the image is formed on the right side of the optical center of mirror or lens, then the distance of the image (v) is positive. Likewise, if the image is formed on the left side of the optical center, ‘v’ is negative.
• The focal lengths (f) of a concave mirror and convex lens are considered positive. The focal lengths of a convex mirror and concave lens are considered negative.
• Heights measured above the principal axis are positive, and below the principal axis are considered negative.
• The image height for a erect image is considered positive, while for a inverted image, it is negative.

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Mirror and Lens are optical instruments that are used to manipulate and focus light in various ways, making them essential components in fields such as photography, astronomy, microscopy, and vision correction. Mirrors and Lenses are the two most critical optical devices that play a vital role in our lives. Whether it’s the mirror we use to check our appearance regularly or the lenses in our eyeglasses, we can’t go a day without; these optical tools serve distinct purposes.

In this article, we will explore what is a mirror and a lens, their types, and ultimately, the key differences between a mirror and a lens to examine their unique characteristics.