Question

A convex mirror has a radius of curvature whose magnitude is 43 cm. The mirror is positioned on a horizontal optical bench with its front surface at 0 cm. A 13.5 cm long fluorescent lamp oriented vertically is placed at +90 cm. What is the focal length of the mirror? Tries 0/5

At what distance from the mirror can we find a sharp image of the lamp? Tries 0/5

How tall is the image of the lamp? Tries 0/5

If the convex mirror were replaced by a plane mirror and the lamp moved to 238 cm from the plane mirror, how tall would the image be?

When an object is placed p = 110 cm in front of a convex mirror the image size is 40% of the object size. What is the focal length of the mirror in cm? Don't forget the sign of the answer.

Answer 1

a) focal length of conves mirror

we have radius of center of curvature of convex mirror

so, the focal length of the mirror will be given as,

using given   we get,

b)

We have,

distance of lamp from the convex mirror

Let,

distance of image of the lamp from the convex mirror,

the relation between for convex mirror is given as,

Using given and calculated   we get,

that is,

image distance ( expressed in three significant figures )

negative sign indicates that the image is located on the opposite side of the mirror with respect to object's location.

c)

we have,

height of the lamp  

Let,

height of the image

the relation between   for convex mirror is given as,

readjusting above equation we get,

using given , and calculated   we get,

d)

the plane mirror does not enlarge or diminish the size of the image compared to the size of the object that is the plane mirror has zero magnification, therefore the height of the image due to the plane mirror is same as the height of the object no matter how far the lamp is placed from the plane mirror,

there,

height of image of the lamp = height of the lamp = 13.5 cm

e)

Now for a new convex mirror we have,

distance of object from the convex mirror =

image is 40 % larger that the object,

Let,

height of the object

height of the image

distance of image from the convex mirror

magnification of the new convex mirror

Image is 40 % larger than height, that means height of the image is 40 % larger that height of the object,

that is,

the magnification in terms of image and object height is defiend as,

so we get,

the magnification in terms of image and object distance is defiend as,

using   and we get,

Let,

  focal length of the new convex mirror

the relation between for convex mirror is given as,

Using calculated and given    we get,