The correct answer is 20 cm. Explanation & Key Takeaways: • To solve this question, we use the mirror formula: 1/f = 1/v + 1/u, where: • f is the focal length of the mirror. • v is the distance of the image from the mirror. • u is the distance of the object from the mirror. • Given: • v = 20 cm (image distance). • u = -10 cm (object distance; negative because the object is placed on the same side as the reflecting surface). • Using the formula: • 1/f = 1/v + 1/u • Substitute the values: 1/f = 1/20 + 1/(-10) • 1/f = 1/20 - 1/10 • Find the LCM: 1/f = (1 - 2)/20 = -1/20 • Thus, f = -20 cm. • The negative sign indicates that the focal length is on the same side as the object, confirming it is a concave mirror. • Therefore, the focal length of the mirror is 20 cm. Related Concepts: • Mirror Formula: • The formula 1/f = 1/v + 1/u is universally applicable for all mirrors (concave, convex, or plane). • It relates the focal length (f), object distance (u), and image distance (v). • Sign convention is crucial: • Distances measured in the direction of the incident light are positive. • Distances measured against the direction of the incident light are negative. • Concave Mirror: • A concave mirror has a reflecting surface that curves inward, resembling the interior of a sphere. • It forms real, inverted images when the object is beyond the focal point and virtual, upright images when the object is inside the focal point. • Applications: Used in headlights, shaving mirrors, and astronomical telescopes. • Image Formation by Concave Mirrors: • If the object is placed: • Beyond the center of curvature: Image is real, inverted, and smaller. • At the center of curvature: Image is real, inverted, and of the same size. • Between the center of curvature and focus: Image is real, inverted, and magnified. • At the focus: Image is highly magnified and formed at infinity. • Between the focus and the pole: Image is virtual, upright, and magnified. • Sign Conventions in Mirrors: • Object distance (u): Always negative for real objects. • Image distance (v): Positive for real images and negative for virtual images. • Focal length (f): Negative for concave mirrors and positive for convex mirrors.