An object of height 3 cm is placed in front of a concave mirror at 10 cm. If the height of the image is also 3 cm, then radius of curvature of the mirror is
Question
An object of height 3 cm is placed in front of a concave mirror at 10 cm. If the height of the image is also 3 cm, then radius of curvature of the mirror is
Solution
The problem can be solved using the mirror formula and the magnification formula in optics.
The mirror formula is 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance.
The magnification formula is -v/u = h'/h, where h' is the height of the image and h is the height of the object.
Given in the problem, the object height h = 3 cm, the image height h' = -3 cm (the negative sign indicates that the image is inverted), and the object distance u = -10 cm (the negative sign indicates that the object is on the same side as the light source).
Substituting these values into the magnification formula gives -v/(-10) = -3/3, which simplifies to v = 10 cm.
Substituting v = 10 cm and u = -10 cm into the mirror formula gives 1/f = 1/10 + 1/(-10), which simplifies to 1/f = 0, so f = infinity.
The radius of curvature R of the mirror is twice the focal length, so R = 2f = 2*infinity = infinity.
Therefore, the radius of curvature of the mirror is infinity, which means the mirror is a plane mirror.
Similar Questions
An object of size 2.0 cm is placed perpendicular to the principal axis of a concave mirror. The distance of the object from the mirror equals the radius of curvature. The size of the image will be ___________.Select an answerA0.5 cmB1.5 cmC1.0 cmD2.0 cm
A mirror at an amusement park shows an upright image of any person who stands 1.9 m in front of it. If the image is three times the person’s height, what is the radius of curvature of the mirror?
A concave mirror forms a real image that is twice the size of the object. If the object is 20 cm from the mirror, the radius of curvature of the mirror must be about:13 cm20 cm27 cm40 cm
A person is standing x cm away from concave security mirror in a store, if the person's image appears to be three times taller than the actual person which is virtual and if the radius of curvature of the mirror is 48 cm, then find x?-12 cm-16 cm-13.33 cm-26.66 cm
An object is placed at the centre of curvature of a concave mirror. The distance between its image and the pole isSelect an answerAequal to fBbetween f and 2fCequal to 2fDgreater than 2f
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.