As per the cartesian sign convention followed for mirrors and lensesa)focal length of concave mirror and concave lens is negativeb)focal length of concave mirror and convex lens is negativec)focal length of convex mirror and convex lens is negatived)focal length of convex mirror and concave lens is negativeCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

the center of curvature and focus lie in front of the

concave mirror, so radius of curvature and focal length are taken as negative in the case of concave mirror.

and center of curvature and focus lies behind the convex mirror, so sign of radius of curvature and focal length are taken as + (positive) in the case of convex mirror. so option C and D is wrong

even in convex lens focal length is taken positive +. so option B IS also wrong

hence correct option is option A

Answer

The focal length of concave mirror and concave lens is negative as it is in front of mirror and lens or on left side  respectively.

Answer

Cartesian Sign Convention for Mirrors and Lenses:

The Cartesian sign convention is a set of rules used to determine the sign (+/-) of various distances and focal lengths in the study of mirrors and lenses. It helps in keeping track of the direction and nature of light rays when they interact with optical devices.

Focal Length of Concave Mirror and Concave Lens:

According to the Cartesian sign convention:
- The principal axis is the reference line and is taken as the positive direction.
- Distances measured along the principal axis are considered positive on one side and negative on the other.
- Distances measured perpendicular to the principal axis are considered positive above the principal axis and negative below it.

For a concave mirror:
- The focus is on the positive side of the mirror.
- The focal length is positive for a concave mirror.

For a concave lens:
- The focus is on the negative side of the lens.
- The focal length is negative for a concave lens.

Focal Length of Concave Mirror and Convex Lens:

For a convex lens:
- The focus is on the positive side of the lens.
- The focal length is positive for a convex lens.

Therefore, the focal length of a concave mirror and a convex lens is positive.

Focal Length of Convex Mirror and Convex Lens:

For a convex mirror:
- The focus is on the negative side of the mirror.
- The focal length is negative for a convex mirror.

For a convex lens:
- The focus is on the positive side of the lens.
- The focal length is positive for a convex lens.

Therefore, the focal length of a convex mirror and a convex lens is positive.

Focal Length of Convex Mirror and Concave Lens:

For a convex mirror:
- The focus is on the negative side of the mirror.
- The focal length is negative for a convex mirror.

For a concave lens:
- The focus is on the negative side of the lens.
- The focal length is negative for a concave lens.

Therefore, the focal length of a convex mirror and a concave lens is negative.

Conclusion:

Based on the Cartesian sign convention, the correct option is 'A' - the focal length of a concave mirror and concave lens is negative. This convention helps in determining the sign of the focal length and keeping track of distances and directions in the study of optics.

Similar Class 10 Doubts

According to the new cartesian sign convention,

According to New Cartesian Sign Convention for a convex lens:A. Distance of the object is negative.B. Distance of the real image is negative.C. Distance of the virtual image is positive.D. Focal length of the lens is positive.

Which one is correct as the new cartesian sign conventions ?

Explain second point of ' New Cartesian Sign Convention '-> " All distances parallel to principal axis are measured from the pole of the mirror."?

Can u say differences about concave mirror and convex mirror and which mirror has v negative and u negative f negative

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