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A concave mirror has a focal length of 15 cm. If an object is placed at a distance of 10 cm from the mirror, what is the position of the image formed?
30 cm behind the mirror
30 cm in front of the mirror
15 cm behind the mirror
20 cm in front of the mirror
30 cm behind the mirror
When an object is placed within the focal length of a concave mirror (less than 15┬аcm), a virtual, erect, and magnified image is formed behind the mirror at a distance of 30┬аcm. This occurs because the reflected rays diverge and appear to meet behind the reflecting surface.
When an object is placed within the focal length of a concave mirror (less than 15┬аcm), a virtual, erect, and magnified image is formed behind the mirror at a distance of 30┬аcm. This occurs because the reflected rays diverge and appear to meet behind the reflecting surface.
This is similar to looking into a makeup or shaving mirror when your face is very close to itтАФyou see an upright, magnified reflection of yourself that appears to be deep inside the glass.
When the object is closer than the focal point, the image goes behind (Virtual, Erect, Magnified).
f1тАЛ=v1тАЛ+u1тАЛ тАФ Mirror formula relating focal length, image distance, and object distance
m=uтИТvтАЛ тАФ Linear magnification formula for spherical mirrors
According to the mirror formula, the relationship between focal length f, object distance u, and image distance v is given by f1тАЛ=v1тАЛ+u1тАЛ. Substituting f=тИТ15┬аcm and u=тИТ10┬аcm following the New Cartesian Sign Convention, we solve for v to get +30┬аcm. The positive sign of v confirms that the image is formed behind the mirror.
A concave mirror has a negative focal length under the standard sign convention.
When object distance is less than focal length (u<f), a virtual and erect image is produced.
A positive image distance (v) indicates that the image is formed behind the mirror.
Provides high magnification for close-up inspection.
Forms virtual images that cannot be projected onto a screen.
Shaving and makeup mirrors
Dentist's head mirrors
Ophthalmoscopes
Calculation: тИТ151тАЛ=v1тАЛ+тИТ101тАЛтЯ╣v1тАЛ=101тАЛтИТ151тАЛ=301тАЛтЯ╣v=+30┬аcm.
Option B is incorrect because a negative image distance would signify a real image in front of the mirror, which only happens when u>f.
A is correct тАФ The image distance calculates to +30┬аcm, meaning a virtual and erect image is formed 30┬аcm behind the concave mirror.
Always double-check signs when applying the mirror formula; object and focal lengths for concave mirrors are negative in real-object scenarios.