A diverging lens has a focal length of magnitude 23.6 cm. (a) Locate the images

Question

A diverging lens has a focal length of magnitude 23.6 cm.

(a) Locate the images for each of the following object distances.

47.2 cm

23.6 cm

11.8 cm

b) Is the image for the object at distance 47.2 real or virtual?

real

virtual    

Is the image for the object at distance 23.6 real or virtual?

real

virtual    

Is the image for the object at distance 11.8 real or virtual?

real

virtual    

(c) Is the image for the object at distance 47.2 upright or inverted?

upright

inverted    

Is the image for the object at distance 23.6 upright or inverted?

upright

inverted    

Is the image for the object at distance 11.8 upright or inverted?

upright

inverted    

(d) Find the magnification for the object at distance 47.2 cm.


Find the magnification for the object at distance 23.6 cm.


Find the magnification for the object at distance 11.8 cm.

Explanation / Answer

Given,

f = -23.6 cm (diverging lens has negative focal length)

(a) Wre have to locate the image for object distances "o"

o1 = 47.2 cm ; o2 = 23.6 cm and o3 = 11.8 cm

Let i1 , i2 and i3 be the corresponding image distances.

We know from lens equation that,

1/f = 1/i + 1/o

i = o x f / ( o - f )

i1 = o1 x f / (o1 - f) = 47.2 x (-23.6) / (47.2 + 23.6) = -15.73 cm

i2 = o2 x f / (o2 - f) = 23.6 x (-23.6) / (23.6 + 23.6) = -11.8 cm

i3 = o3 x f / (o3 - f) = 11.8 x (-23.6) / (11.8 + 23.6) = -7.87 cm

Hence, i1 = -15.73cm ; i2 = -11.8cm and i3 = -7.87 cm

b)The image distance for all the given object distances are negative and hence all the images formed are itual.

47.2 Virtual

23.6 Virtula

11.8 Virtual

c)We know that,

M = -i/o

m1 = -i1/o1 = -(-15.73)/47.2 = 0.33

m2 = -i2/o2 = -(-11.8)/23.6 = 0.5

m3 = -i3/o3 = -(-7.87)/11.8 = 0.66

We notice that the magnification for the given distances are all positive and hence all the images formed for the given object distances are UPRIGHT

47.2 UPRIGHT

23.6 UPRIGHT

11.8 UPRIGHT

d)

m1 = -i1/o1 = -(-15.73)/47.2 = 0.33

m2 = -i2/o2 = -(-11.8)/23.6 = 0.5

m3 = -i3/o3 = -(-7.87)/11.8 = 0.66

Hence, m1 = 0.33 ; m2 = 0.5 and m3 = 0.66

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.