Optics and magnification problems

Question

1.A converging lens has a focal length of 0.48 m. If an object is placed at 0.07 m from the lens, where will its image be located?

2.Is the image virtual or real in the previous question?

3.A concave mirror has a focal length of 0.36 m. If an object produces a real image 0.99 m from the mirror, where is it located?

Answer 1

(1) From 1/f = 1/d_o + 1/d_i, obtain 1/0.48 = 1/0.07 + 1/d_i which gives d_i equal to -0.08195121953 meters with the image in front of the lens.

(2) For d_i < 0, the image is virtual; that is to say, the image is formed on the side of the lens from which the light is incident. Image distance is negative if the image is in front of the lens.

(3) From 1/f = 1/d_o + 1/d_i, write 1/0.36 = 1/d_o + 1/0.99 which gives d_o equal to 0.5657142856 meters.

For d_o >0, the object is real and in front of the mirror. (Note that d_i here is also positive with the real

image in front of the mirror.)