The question asks for the correct mirror formula for spherical mirrors. This is a fundamental formula in optics that relates the object distance, image distance, and focal length of a spherical mirror. We need to recall the standard form of this formula.
C) \(1/v + 1/u = 1/f\). This is the correct and standard mirror formula used in optics for spherical mirrors.
The question asks for the formula for magnification produced by a spherical mirror. Magnification is defined as the ratio of the height of the image to the height of the object. It can also be expressed in terms of image distance and object distance. We need to recall the standard sign convention used in optics for spherical mirrors.
Correct Option: D) The magnification produced by a spherical mirror is given by \(m = -v/u\). This formula correctly relates the image distance (\(v\)) and object distance (\(u\)) with the magnification (\(m\)), incorporating the sign convention to indicate the image's orientation.
To determine the nature of the image formed by a concave mirror when an object is placed at its center of curvature, we can use ray tracing rules or the mirror formula. Ray tracing provides a visual understanding of the image characteristics.
A) Real, inverted, and same size as the object. This accurately describes the image formed when an object is placed at the center of curvature of a concave mirror, as derived from ray tracing and mirror formula principles.
This question tests the understanding of image formation by a concave mirror, specifically when the object is placed at its focus. We can determine the image location using ray diagrams or the mirror formula.
Correct Option: B) Infinity
The question asks about the nature of the image formed by a concave mirror when an object is placed between its pole and focus. This is a standard case in ray optics for concave mirrors, and understanding the ray tracing rules or the mirror formula helps determine the image characteristics.
D) Virtual, erect, and magnified - As explained in the step-by-step analysis, when an object is placed between the pole and focus of a concave mirror, the image formed is virtual, erect, and magnified. This is the principle behind a shaving mirror or a dentist's mirror.
To find the position of the image formed by a concave mirror, we use the mirror formula, which relates the focal length of the mirror to the object distance and the image distance. We must also follow the sign conventions for spherical mirrors.
For a concave mirror, the focal length is taken as negative.
The mirror formula is given by:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]Substitute \(f = -10 \text{ cm}\) and \(u = -30 \text{ cm}\) into the mirror formula:
\[ \frac{1}{-10} = \frac{1}{v} + \frac{1}{-30} \]Rearrange the formula to solve for \(1/v\):
\[ \frac{1}{v} = \frac{1}{-10} - \frac{1}{-30} \]\[ \frac{1}{v} = -\frac{1}{10} + \frac{1}{30} \]The common denominator for 10 and 30 is 30.
\[ \frac{1}{v} = -\frac{3}{30} + \frac{1}{30} \]\[ \frac{1}{v} = \frac{-3 + 1}{30} \]\[ \frac{1}{v} = \frac{-2}{30} \]\[ \frac{1}{v} = -\frac{1}{15} \]Invert both sides to find \(v\):
\[ v = -15 \text{ cm} \]The negative sign for \(v\) indicates that the image is formed in front of the mirror (on the same side as the object), and its distance from the mirror is 15 cm.
C) 15 cm in front of the mirror