A 60 pair of binoculars has an objective focal length of 26

A 6.0 × pair of binoculars has an objective focal length of 26cm. If the binoculars are focused on an object 3.5 m away (from the objective), what is the magnification? (The 6.0 × refers to objects at infinity). Note that binoculars produce upright images. Please show and explain your work! Thanks!

Solution

Focal Length of eyepiece

f_e = f_o/M =26/6

f_e=4.33 cm

From thin lens formula

1/f_o = 1/d_i + 1/d_o

1/0.26 =1/d_i + 1/3.5

d_i=0.281 m =28.1 cm

Magnification

M =(h/f_e)/(h/d_i)=d_i/f_e

M=28.1/4.33

M =6.48 =6.5 X (approx)