Physics🎊🎊🎊Reflection of spherical mirror & Plane mirror?

In fig. , the radius of curvature of the concave mirror Y is 16cm, the plano-mirror X is situated at 10cm from the concave mirror at 45° with the principal axis of the concave mirror. A light source P is located 14cm below the plano-mirror and a ray PX incident on the plano-mirror vertically upward.

(a) Where is the image of the source P after the reflections from the two mirrors?

(b) Show the ray diagram of the formation of the image.

Thanks in advance for helping generously!!!

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1 Answer

  • 3 years ago
    Favorite Answer

    For spherical mirrors:

    f = -r/2, where f is the focal length and r is the radius of curvature. Here f = -16cm / 2 = -8cm.

    For your setup, the 45 degree mirror does nothing but change the optical axis from vertical to horizontal. To calculate the image position on the optical axis, we use the mirror equation:

    1/f = 1/O + 1/I (f, O, I in cm)

    1/(-8) = 1/(10+14) + 1/I

    -1/8 - 1/24 = -1/6 = 1/I

    I = -6cm from the mirror, which places it on the horizontal portion on the left side of the mirror. (It is a negative value because this is a formulation of the lens equation, and the negative value indicates reflection)

    To draw the ray diagram, simply draw three lines from P - one vertical, and one a bit to each side. Reflect them at the 45 degree mirror rotating the directions appropriately, then continue them to the spherical mirror. From the mirror they will intersect at a point 6cm to the left.

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