A glowing electric light bulb placed 15 cm from a concave spherical mirror produces a real image

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A glowing electric light bulb placed 15 cm from a concave...

A glowing electric light bulb placed $15 \mathrm{cm}$ from a concave spherical mirror produces a real image $8.5 \mathrm{cm}$ from the mirror. If the light bulb is moved to a position $25 \mathrm{cm}$ from the mirror, what is the position of the image? Is the final image real or virtual? What are the magnifications of the first and final images? Are the two images inverted or upright?

Key Concepts

Image Orientation (Inversion)

Image orientation refers to whether an image is inverted or upright relative to the object. In spherical mirror setups, real images (formed when the object is beyond the focal point) are typically inverted, while virtual images (formed when the object is within the focal length) are upright. This characteristic is essential for understanding the behavior of optical imaging systems.

Real vs. Virtual Images

Real images are formed when reflected rays actually converge, meaning the image can be projected on a screen; they are typically associated with a negative image distance in the mirror formula. Virtual images, on the other hand, are formed by the apparent divergence of rays and cannot be projected onto a screen, generally corresponding to a positive image distance. Understanding the nature of the image is essential in optical design and analysis.

Magnification in Spherical Mirrors

Magnification, defined as m = -q/p, indicates the ratio of the image height to the object height and provides information on how much larger or smaller the image is relative to the object. The negative sign in the magnification formula helps indicate the image inversion, linking intensity with the reality (inverted or upright) of the image.

Mirror Formula

The mirror formula (1/f = 1/p + 1/q) is a fundamental relationship in geometric optics for spherical mirrors, relating the focal length (f) of the mirror to the object distance (p) and the image distance (q). This equation is the starting point for calculating image positions when the object’s location and the mirror’s focal length are known.

Sign Conventions

Sign conventions are crucial in mirror problems to determine the correct signs (positive or negative) for distances and focal lengths. They differentiate between situations where images are formed on the same side of the mirror as the object (typically real images) or the opposite side (virtual images), and they help in accurately applying the mirror formula.

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