Concave mirror

Question

A converging (concave) mirror has a focal length of 11.0 cm with and an object 6.00 cm away from the mirror.

A-The distance to the image is: ___ cm

B- The magnification is ____x 

C- The image produced will be:

 

real?

Or

virtual?

 

 

Answer 1

a)

Focal Length f = 11 cm

Distance from the mirror to the object d_object = 6 cm

Distance to the image = d_image

Formula : (1/f) = (1/d_object) + (1/d_image)

(1/11) = (1/6) + (1/d_image)

(1/d_image) = (1/11) - (1/6)

Rewrite the expression with common denominator.( LCM of 11,6 is 66 )

(1/d_image) = (6-11)/66 = -5/66 = -1/13.2

d_image = -13.2 cm.

A negative image distance (d_image) corresponds to an image located behind the mirror.

Virtual images will have negative d_i values.

Distance to the image is 13.2 cm (Image located behind the mirror).

Answer 2

b)

The magnification M = - (d_image)/(d_object)

M = - (-13.2)/6 = 2.2

The Magnification is 2.2.

Answer 3

c)

Properties of concave mirror :

A positive image distance (d_image) corresponds to an image location on the same side of the mirror as the object. Real images will always be characterized by positive d_image values.

A negative image distance (d_image) corresponds to an image located behind the mirror.Virtual images will have negative d_image values.

As d_image is - 13.2 cm , which is negative value.

So image produced will be Virtual image.