2. ALPINE SKI HOUSE
ALPINE SKI HOUSE
LET’S LEARN
Magnification is the process of enlarging something in appearance
only, but not in size. This enlargement is quantified by a calculated
number also called “magnification”. To compute for this number, you
need to use magnification equation which relates the ratio of the image
distance and object distance to the ratio of the image height(hi) and the
object height(ho).
hi
ho
= -
di
do
; hido = - diho
2
3. ALPINE SKI HOUSE 3
where,
M = the magnification of the image
hi = height of the image
ho = height of the object
di = distance of the image from the lens
do = distance of the object from the lens
4. ALPINE SKI HOUSE 4
Example 1.
A girl is 165.1 cm(5’5”ft) tall and 68.2 cm from a convex lens. Her
real image is formed 37.8 cm from the lens.
a. What is the height of the image?
b. What is the focal length of the lens?
Given: Find:
ho = 165.1 cm a. hi
do = 68.2 cm b. f
di = 37.8 cm
5. ALPINE SKI HOUSE 5
Solution a:
Using the magnification equation, determine the height of the image.
hi
ho
= -
di
do
;
hi
ho
= -
di
do
= hido = -diho ; hi =
−𝑑𝑖ℎ𝑜
𝑑𝑜
hi = - hodi
do
hi = - (161.1 cm)(37.8 cm) = - 91.51 cm
68.2 cm
Interpretation: The height of the image is -91.51 cm
6. ALPINE SKI HOUSE 6
Solution b:
Using the mirror equation, determine the focal length of the lens.
1
𝑓
=
1
𝑑𝑜
+
1
𝑑𝑖
f =
𝑑𝑜𝑑𝑖
𝑑𝑖+𝑑𝑜
f =
(68.2 𝑐𝑚)(37.8 𝑐𝑚)
37.8 𝑐𝑚 +(68.2 𝑐𝑚)
= 24.32 cm
Interpretation: The focal length of the lens is 24.32 cm.
7. ALPINE SKI HOUSE 7
Example 2.
A convex lens has a focal length of 10 cm. An 8 cm high
object is located 35 cm in front of the lens.
f =10 cm r = 20 cm
ho = 8cm
do =35 cm
di = 14 cm
m = - 0.4
a. What is the image distance?
b. What is the magnification?
c. What is the image height?
8. ALPINE SKI HOUSE 8
a. What is the image distance?
di =
𝑓𝑑𝑜
𝑑𝑜
−𝑓
di =
(10 𝑐𝑚)(35 𝑐𝑚)
35 𝑐𝑚 −10 𝑐𝑚
=
350 𝑐𝑚2
25 𝑐𝑚
= 14 cm
9. ALPINE SKI HOUSE 9
b. What is the magnification?
m = -
𝑑𝑖
𝑑𝑜
m = -
14 𝑐𝑚
35𝑐𝑚
= - 0.4
For magnifications m < 1,the image is reduced and for m > 1, the image
is enlarged. Moreover if m is positive, the image and the object have
the same orientation, otherwise, they are inverted with respect to each
other.
The negative sign denotes an inverted image. Therefore, it is real,
reduced and inverted.
10. ALPINE SKI HOUSE 10
c. What is the image height?
hi =
−𝑑𝑖ℎ𝑜
𝑑𝑜
hi = -
(14 𝑐𝑚)(8𝑐𝑚)
35 𝑐𝑚
hi =
112𝑐𝑚2
35 𝑐𝑚
= -3. 2 cm
11. ALPINE SKI HOUSE 11
Example 3.
A converging lens formed a real image that is 15.0 cm from it. If the
focal length of the lens is 10 cm, where is the object placed? What is the
magnification?
do =
𝑓𝑑𝑖
𝑑𝑖 −𝑓
do =
(10 𝑐𝑚) (15 𝑐𝑚)
15 𝑐𝑚 −10 𝑐𝑚
=
150 𝑐𝑚2
5 𝑐𝑚
= 30 cm
The object is located 30 cm in front of the mirror.
m = -
𝑑𝑖
𝑑𝑜
= -
15 𝑐𝑚
30 𝑐𝑚
= - 0. 5 cm
