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14
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2. 14
14.1
ˈ F F F F F
F ˈ F
- ˈ F
- F 3x 108 /
- 1 ʾ F 1 ʾ
- F F F F
- F
14.2 F
ˈ F
1. F F F
2. (i) F F (r)
i r
i r i r i r
F
F
i r
F
i r i r
F F F
F ˆ F www.schoolDD.com 1

3. 14.2.1
F F F F
F
F F F
F F F
F F F F
F F
Q r B r Q
i
y y
i r
P A P
s s
୅୆ ୅୆
tan i = ୱ
tan r = ୱᇲ
i=r tan i = tan r
୅୆ ୅୆
ୱ
= ୱᇲ
F
s =s y =y
s =
s =
y =
y =
1. (s ) F (s)
2. (y ) F (y)
F ˆ F www.schoolDD.com 2

4. 3. ˈ F FF F F F
F F F F F
F 1
F F F F F F F
a i2
a r2
h b r1
i1
b
F F F F F F F
F
F F
i = F r
F i1 = r1 i2 = r2
h = a + a + b + b = 2(a + b)
= a+b
= h/2
F = Ans
14.2.2 F F
F F
F
F F
F
C F V V F C
r
i
i
f r f
R R
F
F ˆ F www.schoolDD.com 3

5. C ˈ F F
R ˈ F
F CV ˈ F
F ˈ F F
f ˈ
.......... ‫܀‬
f=
૛
F F F F F
R R
f f
3
3
C F V V F C
s s
s
s
1. CV F F
F F
2. F F F F
CV
3. F F F C F F
F
4. F F F F
F F
5. F ( F ) F F
F F F F
F ˆ F www.schoolDD.com 4

6. F
1. s=
s=
C F
2. s>R
C F F F
3. s=R
C F F F
F ˆ F www.schoolDD.com 5

7. 4. f<s<R
C F F F F
5. s=f
C F F F
6. s<f
C F F F F
7. F
C F F F F
F ˆ F www.schoolDD.com 6

8. 1. s=
s=
F C F
2. s>R
F C F F
3. s=R
F C F F
4. f<s<R
F C F F
F ˆ F www.schoolDD.com 7

9. 5. s=f
F C F F
6. s<f
F C
F F
7. F
F C F F F
F
1. F F F F
F F F F
2. F F F
F
F ˆ F www.schoolDD.com 8

10. F F (f) (s) (s ) F
R
Q
y
C P i
P y r
Q
s
s
F = F FF
૚ ૚ ૚
= +
܎ ‫ܛ‬ ‫ܛ‬ᇲ
‫ܡ‬ᇲ ‫ܛ‬ᇲ
M = = M
‫ܡ‬ ‫ܛ‬
F F F F +,- f,s s
1. f ( ) ˈ + ˈ ( F)
ˈ - ˈ ( )
2. s ( ) ˈ + ˈ F F
ˈ - ˈ F
3. s ( ) ˈ + ˈ F F
ˈ - ˈ F
4. M ( ) ˈ + ˈ
ˈ - ˈ
F 2
10 F F F ˈ 30 F 20
F ˈ F ˈ F F
. ˈ F . ˈ
F ˆ F www.schoolDD.com 9

11. . ˈ F
y = 10
C F
f = 10
R = 20
s = 30
ଵ ଵ ଵ
s = + f = +10, s = +30
୤ ୱ ୱᇲ
ଵ ଵ ଵ
= +
ଵ଴ ଷ଴ ୱᇲ
s = 15 cm ˈ + F Ans
୷ᇲ ୱᇲ
y M= =
୷ ୱ
ୱᇲ ଵହ
y =y = 10
ୱ ଷ଴
y = 5 cm. Ans
F F F F F
. ˈ
y = 10
F C
s = 30
f = 10
R = 20
ଵ ଵ ଵ
s = + f = -10, s = +30
୤ ୱ ୱᇲ
F ˆ F www.schoolDD.com 10

12. ଵ ଵ ଵ
= +
ିଵ଴ ଷ଴ ୱᇲ
s = -7.5 ˈ - Ans
୷ᇲ ୱᇲ
y M= =
୷ ୱ
ୱᇲ ି଻.ହ
y =y = 10
ୱ ଷ଴
y = -2.5 cm. Ans ( F ˈ )
F F F F F
F 3
F F F F F 20 cm. F 60 cm.
F . F
F C
s = 20
s=?
f = 30
R = 60
ଵ ଵ ଵ ୖ
s = + f= = -30, s = -20
୤ ୱ ୱᇲ ଶ
ଵ ଵ ଵ
= +
ିଷ଴ ୱ ିଶ଴
s = 60 cm ˈ + F Ans
F 4
FF F F F F
F F
F ˆ F www.schoolDD.com 11

13. C F
14.3
14.3.1
F F F F F
F F F F
F
1 θ1 F F
2
θ2
F
F F F F F F F
ୱ୧୬ θభ
= F
ୱ୧୬ θమ
n
ୡ
F F (c) (n) , n =
୴
ଵ
c n ‫ן‬
୴
F f
ୱ୧୬ θభ ୴భ
F =
ୱ୧୬ θమ ୴మ
ୡ/୬భ
=
ୡ/୬మ
ୱ୧୬ θభ ୬మ
=
ୱ୧୬ θమ ୬భ
F ˆ F www.schoolDD.com 12

14. FF ‫ ܖܑܛ‬ી૚ ‫ܞ‬૚ ‫ܖ‬૛
= =
‫ ܖܑܛ‬ી૛ ‫ܞ‬૛ ‫ܖ‬૚
θ1 = 1
θ2 = 2
v1 = 1
v2 = 2
n1 = 1
n2 = 2
F 5
F F F 30° F F
ˈ F
F
θ1
n1 = 1.0
n2 = 1.3
θ2
ୱ୧୬ θభ ୬మ
=
ୱ୧୬ θమ ୬భ
ୱ୧୬ ଷ଴ ଵ.ଷ
=
ୱ୧୬ θమ ଵ.଴
଴.ହ
sin θ2 = = 0.38
ଵ.ଷ
θ2 = sin-1 0.38 = 22.6° Ans
F ˆ F www.schoolDD.com 13

15. F 6
F
45
A
30
B
F F
. A F B
. A F F B
. F F
. A F F B
. F F
14.3.2 F
F F F F
F θ2 F F θ1 F θ1
F θ2 = 90° F θc
F θc
F
2 n2 θ2 = 90° ୱ୧୬ θభ ୬మ
ୱ୧୬ θమ
= ୬భ
1 n1 > n 2
θ1 = θc
ୱ୧୬ ஘ౙ ୬మ
ୱ୧୬ ଽ଴
= ୬భ
( θ1 = θc , θ2 = 90° )
୬మ
sin θୡ =
୬భ
F ˆ F www.schoolDD.com 14

16. F
ˈ F F θ1 > θc
F F F ˈ F (
= F )
F
2 n2
1 n1 > n 2 θ1 > θc
θ1 θ2 θ2 = θ1
F 7
F F 1.5 F ˈ 1.0
F
n2 = 1 θ2 = 90°
F n1 = 1.5 F
θ1 = θc
F F F
-->
ୱ୧୬ θభ ୬మ
ୱ୧୬ θమ
= ୬భ
ୱ୧୬ ஘ౙ ଵ
ୱ୧୬ ଽ଴
= ଵ.ହ
sin θୡ = 0.67
θc = 42° Ans
F ˆ F www.schoolDD.com 15

17. F 8
F ˈ 53º
8
F ˈ 3 x10 m/s F ˈ 1.0
F
n2 = 1 θ2 = 90°
n1 = ?
θ1 = θc = 53°
ୱ୧୬ θభ ୬మ
ୱ୧୬ θమ
= ୬భ
ୱ୧୬ ହଷ ଵ
ୱ୧୬ ଽ଴
= ୬భ
ଵ
4/5 = ୬భ
n1 = 5/4
ୡ
F n= ୴
ୡ
v1 = ୬భ
= 3x108 x 4/5
v1 = 2.4x108 m/s Ans
14.3.3
F F F F
F F F F
F F F
F F F F F F F
F ˆ F www.schoolDD.com 16

18. F
n2 A B θ2
n1 θ1 s s = ( )
θ2
C s = ( )
s
θ1
ୱ୧୬ θభ ୬మ
D =
ୱ୧୬ θమ ୬భ
n1 > n 2 2 > 1
∆ ABC ∆ ABD
୅୆
tan 1 = ୅ୈ
--------- 1
୅୆
tan 2 = ୅େ
--------- 2
୲ୟ୬ θభ ୅େ ୱᇲ
1/2 , ୲ୟ୬ θమ
= ୅ୈ
= ୱ
‫ܛ‬ᇲ ‫ ܖ܉ܜ‬ી૚
=
‫ܛ‬ ‫ ܖ܉ܜ‬ી૛
1 2 F tan sin F
‫ܛ‬ᇲ ‫ ܖܑܛ‬ી૚ ‫ܖ‬૛
= =
‫ܛ‬ ‫ ܖܑܛ‬ી૛ ‫ܖ‬૚
F 9
F 3m F ˈ 1.0 4/3
F F
. 60° .
F ˆ F www.schoolDD.com 17

19. . 60°
F
θ2
n2 = 1 60°
n1 = 4/3 θ1 s =?
s=3
60° θ2 = 30°
ୱᇲ ୲ୟ୬ θభ
ୱ
= ୲ୟ୬ θమ
------- 1
ୱ୧୬ θభ ୬మ
F s, θ2 θ1 =
ୱ୧୬ θమ ୬భ
ୱ୧୬ θభ ଵ
=
ଵ/ଶ ସ/ଷ
8
3
sin θ1 = 3/8 θ1 tan θ1 = 3/√55
√55
F 1 F
ୱᇲ ୲ୟ୬ θభ
ୱ
= ୲ୟ୬ θమ
ୱᇲ ଷ/√ହହ
ଷ
= ଵ/√ଷ
s = 2.1 m Ans
.
1 2 F tan sin
ୱᇲ ୱ୧୬ θభ ୬మ
= =
ୱ ୱ୧୬ θమ ୬భ
ୱᇲ ୬మ
=
ୱ ୬భ
F ˆ F www.schoolDD.com 18

20. ୱᇲ ଵ
=
ଷ ସ/ଷ
s = 2.25 m Ans
F 10
1 F F F F
1 4/3
F
s=1
n1 = 1
n2 = 4/3
ୱᇲ ୱ୧୬ θభ ୬మ
= =
ୱ ୱ୧୬ θమ ୬భ
ୱᇲ ୬మ
=
ୱ ୬భ
ୱᇲ ସ/ଷ
=
ଵ ଵ
s = 1.33 m Ans
14.3.4 F F
F F F F F F 2 F F F
F ˈ F F F F
F F F
F F F F F F F F F F F F
F ˆ F www.schoolDD.com 19

21. F F
C1 F1 O F2 C2 C1 F1 O F2 C2
r r
i i
f f f f
R R R R
F F F
C1 C 2 ˈ F F
O ˈ F F F F F F F
O F F F
F C1 C 2 ˈ F
F1 , F 2 ˈ
f ˈ
‫܀‬
f= R ˈ F F
૛
F F F F F
3
3
C1 F1 O F2 C2 C1 F1 O F2 C2
s
f f
R R
s s s
F ˆ F www.schoolDD.com 20

22. 1. F F F
2. F FO F
3. F F F
4. ˈ F F F
5. ( F ) ˈ F F F F
F F
F
1. s= ∞
s=
O
F
C F F C
F F
2. s>R
O F F
C F F C
3. s=R
F F
C F O F C
4. f < s <R
F F F
C F O F C
F ˆ F www.schoolDD.com 21

23. 5. s=f
C F O F C F
6. s<f
F F F
C F O F C
7. F F(s=0)
F F F
C F O F C
F F
1. s= ∞
s=
F
C F O F C F F F
F ˆ F www.schoolDD.com 22

24. 2. s>R
O F F
C F F C
3. s=R
F F
C F O F C
4. f<s<R
F F
C F O F C
5. s=f
F F
C F O F C
6. s<f
O F F
C F F C
F ˆ F www.schoolDD.com 23

25. 7. F F (s=0)
F F F
C F O F C
F
1. F F F F
F F F F F
2. F F F F F F F
F F (f) (s) (s ) F
Q R
y F P C
P O
y
Q
f
s s
F F FF
∆ OPQ F ∆ OP Q
୷ᇲ ୱᇲ
F = -----1
୷ ୱ
∆ FOR F ∆ FP Q
୷ᇲ ୱᇲ ି୤
F = -----2
୷ ୤
ୱᇲ ୱᇲ ି୤
1 2, =
ୱ ୤
૚ ૚ ૚
= +
܎ ‫ܛ‬ ‫ܛ‬ᇲ
F ˆ F www.schoolDD.com 24

26. ‫ܡ‬ᇲ ‫ܛ‬ᇲ
M = + M
‫ܡ‬ ‫ܛ‬
F F F F +,- f,s,s
1. f ( ) ˈ + ˈ ( F )
ˈ ˈ ( F F)
2. s ( ) ˈ + ˈ F F F
ˈ - ˈ F F
3. s ( ) ˈ + ˈ F F
ˈ - ˈ F F F
4. M ( ) ˈ + ˈ
ˈ ˈ
F
F F f,s,s ,y,y M F F
F F F F F
F F = F F F =
F 11
10 cm. F F F ˈ 30cm. F 10cm. F
F ˈ F ˈ F F . ˈ F . ˈ F F
. F
F C
s f
ଵ ଵ ଵ
s = + f = +10, s = +30
୤ ୱ ୱᇲ
ଵ ଵ ଵ
= +
ଵ଴ ଷ଴ ୱᇲ
F ˆ F www.schoolDD.com 25

27. s = 15 ˈ + F Ans
୷ᇲ ୱᇲ
y M= =
୷ ୱ
ୱᇲ ଵହ
y =y = 10
ୱ ଷ଴
y = 5 cm. Ans
F F F F F
. F F
C F
f
s
ଵ ଵ ଵ
s = + f = -10, s = +30
୤ ୱ ୱᇲ
ଵ ଵ ଵ
= +
ିଵ଴ ଷ଴ ୱᇲ
s = -7.5 ˈ - F F Ans
୷ᇲ ୱᇲ
y M= =
୷ ୱ
ୱᇲ ି଻.ହ
y =y = 10
ୱ ଷ଴
y = -2.5 cm. Ans ( F ˈ )
F F F F F
F ˆ F www.schoolDD.com 26

28. F 12
F 2 4 5 F F F ( F F F F F
) 6 cm. F F F F
. F F F 7 cm.
. F F F 20 cm.
f=5
f=4
s = 6 cm
F F F F F F F ˈ F
F
ଵ ଵ ଵ
s = + f = +4, s = +6
୤ ୱ ୱᇲ
ଵ ଵ ଵ
= +
ସ ଺ ୱᇲ
s = 12 ˈ + F
F 12 cm ˈ F
. F F F F 7 cm
F F F ˈ 12-7 = 5 cm
F s = -5 cm ˈ F F
F
ଵ ଵ ଵ
s = + f = +5, s = -5
୤ ୱ ୱᇲ
ଵ ଵ ଵ
= +
ହ ିହ ୱᇲ
s = 2.5 ˈ + F
F ˈ F F 2.5 cm Ans
F ˆ F www.schoolDD.com 27

29. . F F F F 20 cm
F F F F ˈ 20-12 = 8 cm
F s = 8 cm ˈ F F F
F
ଵ ଵ ଵ
s = + f = +5, s = +8
୤ ୱ ୱᇲ
ଵ ଵ ଵ
= +
ହ ଼ ୱᇲ
s = 13.33 ˈ + F
F ˈ F F 13.33 cm Ans
14.4
14.4.1
F F F ˈ F F
F F
F
θr θv
> F
F
F
F F F F
ୱ୧୬θభ λభ
ୱ୧୬θమ
= FF θ2 ‫ ן‬λଶ
λమ
F F F F
14.4.2 F
F ˈ F F2 F
F F F F F F
F ˆ F www.schoolDD.com 28

30. F
F
F
F
F
F
F
F
F F
F
F
F
F ˈ F F F ˈ
F ˈ F
14.4.3
ˈ F F
F F F F F F F F ˈ F F
F
F ˆ F www.schoolDD.com 29

31. 14.5 F
ˈ F F F
F
1. F F F F F F F F
F ˈ (lm) F F F F F F 40 F
F 2,700 500
2. F E F F F (F) F F (A) F ˈ
F (lx)
۴ A F ˈ m2
E =
‫ۯ‬ F F ˈ lm
F 13
F F F 40 F F F F
F F F 3x3x3
3
3
3
F F = 500 lm
F F = 500 lm
୊
E= ୅
୊ F
E F= ୅
ହ଴଴
= ଷ୶ଷ୶ହ
E F = 11.11 lm Ans
୊
E = ୅ F F
ଶ଻଴଴
= ଷ୶ଷ୶ହ
E F = 60 lm Ans
F F F F F 6 F Ans
F ˆ F www.schoolDD.com 30

32. 14.6
F F F F F F F F
ʽF F F
F ˈ F
F F F F F F F
F F F F F 25 F
F F
F F (s = ) F F
F F F F F F F
F 25
25 cm
D
s=
F
F
F F F F F F
F F F F
s=
D=s
F ˆ F www.schoolDD.com 31

33. F F F
ଵ ଵ ଵ
= +
୤ ୱ ୱᇲ
s= s =D ˈ FF F
ଵ ଵ ଵ
F = +
୤ ஶ ୈ
f=D=s
F F F (s = 25 cm.) F
F (s = )
F
25 cm
D
s=
F
F F F 25 cm. F
F F F F 25 cm. F
s = 25 cm
D=s
F ˆ F www.schoolDD.com 32

34. F F
ଵ ଵ ଵ
= +
୤ ୱ ୱᇲ
s = 25 cm s =D ˈ F F F F
ଵ ଵ ଵ
F = +
୤ ଶହ ୈ
F 14
F F FF F F F F F
F 3 F F F F
ˈ F F F F F
ଵ ଵ ଵ
= +
୤ ୱ ୱᇲ
s=∞ s = -3 m ˈ
ଵ ଵ ଵ
F = +
୤ ஶ ିଷ
f = -3 m Ans
F ˆ F www.schoolDD.com 33

35. 14.7
ˈ F F F
F F F F F F
F F F F F
F F F
F
F F F F F F F
ˈ
F
F
F F F F
F F F
F
F
F ˆ F www.schoolDD.com 34

36. F F F F F F F F
F F FF
F F F
F
F F F F
F 15
. ˈ
?
1. 2. 3. 4.
. ˈ
?
1. 2. F 3. 4.
?
. F
? ? ?
F
F F
F ˆ F www.schoolDD.com 35