Question

Solve the following quadratic equations by factorization: $\frac{x-1}{x-2}+ \frac{x-3}{x-4}=3\frac{1}{3}$, x≠2, 4

Answer 1

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Refer to the attachment for Answer ✨

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Answer 2

Answer:

a) When the beam is incident on the lens from medium μ

1

.

Then

v

μ

2

−

u

μ

1

=

R

μ

2

−μ

1

or

v

μ

2

−

(−∞)

μ

1

=

R

μ

2

−μ

1

or

v

1

=

μ

2

R

μ

2

−μ

1

or v=

μ

2

−μ

1

μ

2

R

Again, for 2ns refraction,

v

μ

3

−

u

μ

2

=

R

μ

3

−μ

2

or,

v

μ

3

=−[

R

μ

3

−μ

2

−

μ

2

R

μ

2

(μ

2

−μ

1

)]

⇒−[

R

μ

3

−μ

2

−μ

2

+μ

1

]

or, v=−[

μ

3

−2μ

2

+μ

1

μ

3

R

]

So, the image will be formed at =

2μ

2

−μ

1

−μ

3

μ

3

R

b) Similarly for the beam from μ

3

medium the image is formed at

2μ

2

−μ

1

−μ

3

μ

1

R

.