Question

An object is 12 cm in front of a convex mirror with a center/radius of a curvature of 6 cm. The characteristics of the image are___A. real, inverted at a distance of 12 cmB. virtual, upright at a distance of 2.4 cmC. real, upright at a distance of 4 cmD. virtual, inverted at a distance of 6 cm Must follow GRESA format.Given:Required:Equation(s) Needed:Solution:Final Answer:L-ocation:O-rientation:S-izeT-ype

Answer 1

Given data:

* The radius of curvature of the convex mirror is R = 6 cm.

* The distance of the object from the convex mirror is u = - 12 cm.

Required: The nature of the image formed.

Equations needed:

The mirror formula:

`(1)/(v)+(1)/(u)=(1)/(f)`

The magnification formula:

`m=-(v)/(u)=(h_i)/(h_o)`

Solution:

The focal length of the convex mirror is,

`\begin{gathered} f=(R)/(2) \\ f=(6)/(2) \\ f=3\text{ cm} \end{gathered}`

The distance of the image formed is,

`\begin{gathered} (1)/(v)+(1)/(u)=(1)/(f) \\ (1)/(v)+(1)/((-12))=(1)/(3) \\ (1)/(v)-(1)/(12)=(1)/(3) \\ (1)/(v)=(1)/(3)+(1)/(12) \end{gathered}`

By simplifying,

`\begin{gathered} (1)/(v)=(4+1)/(12) \\ (1)/(v)=(5)/(12) \\ v=(12)/(5) \\ v=2.4\text{ cm} \end{gathered}`

The positive value of image distance indicated that the virtual image is formed.

By the magnification formula,

`\begin{gathered} m=(-(2.4))/(-12) \\ m=0.2 \end{gathered}`

The positive value of magnification indicates that the upright image is formed.

The value of the magnification is less than 1, thus, a small size (diminished) image is formed.

Final Answer:

Location - 2.4 cm behind the convex mirror

Orientation - Upright

Size - Small size (or diminished)

Type - Virtual

Hence, option B is the correct answer.