Vật lý Lớp 9: Chứng MInh Ảnh thật : 1/f = 1/d + 1/d’ Thấu kính hội tụ :

Câu hỏi:
Giúp em bài tập về nhà Vật lý lớp 9 câu hỏi như sau: Chứng MInh
Ảnh thật : 1/f = 1/d + 1/d’
Thấu kính hội tụ :
Ảnh ảo : 1/f = 1d – 1d’
TKPK : 1/f = 1d’ – 1/d

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Trả lời 1:
Gia Sư Hoàng Khang gữi câu trả lời dành cho bạn:

XÉT VỚI THẤU KÍNH HỘI TỤ:

Hình L1 (ảnh thật)

Ta có:

+ $\mathrm{\Delta }OAB\text{~}\mathrm{\Delta }O{A}^{\prime }{B}^{\prime }$

$\Rightarrow {\displaystyle \frac{AB}{A^{\prime }{B}^{\prime }}}={\displaystyle \frac{OA}{O{A}^{\prime }}}$ (1)

+ $\mathrm{\Delta }{F}^{\prime }IO\text{~}\mathrm{\Delta }{F}^{\prime }{B}^{\prime }{A}^{\prime }$

$\Rightarrow {\displaystyle \frac{I\mathrm{O}}{A^{\prime }{B}^{\prime }}}={\displaystyle \frac{F^{\prime }O}{F^{\prime }{A}^{\prime }}}$ (2)

Mà $IO=AB$

Từ (1) và (2) ta suy ra:

$\begin{array}{l}{\displaystyle \frac{OA}{O{A}^{\prime }}}={\displaystyle \frac{F^{\prime }O}{F^{\prime }{A}^{\prime }}}\iff {\displaystyle \frac{OA}{O{A}^{\prime }}}={\displaystyle \frac{F^{\prime }O}{O{A}^{\prime }–F^{\prime }O}}\\ \iff {\displaystyle \frac{O{A}^{\prime }}{OA}}={\displaystyle \frac{O{A}^{\prime }–F^{\prime }O}{F^{\prime }O}}={\displaystyle \frac{O{A}^{\prime }}{F^{\prime }O}}–1\\ \Rightarrow {\displaystyle \frac{O{A}^{\prime }}{OA}}={\displaystyle \frac{O{A}^{\prime }}{F^{\prime }O}}–{\displaystyle \frac{O{A}^{\prime }}{O{A}^{\prime }}}\\ \Rightarrow {\displaystyle \frac{1}{OA}}={\displaystyle \frac{1}{F^{\prime }O}}–{\displaystyle \frac{1}{O{A}^{\prime }}}\\ \Rightarrow {\displaystyle \frac{1}{F^{\prime }O}}={\displaystyle \frac{1}{OA}}+{\displaystyle \frac{1}{O{A}^{\prime }}}\end{array}$

Hay ${\displaystyle \frac{1}{f}}={\displaystyle \frac{1}{d}}+{\displaystyle \frac{1}{d^{\prime }}}$ (ĐPCM)

Hình L2 (ảnh ảo)

+ $\mathrm{\Delta }OAB\text{~}\mathrm{\Delta }O{A}^{\prime }{B}^{\prime }\Rightarrow {\displaystyle \frac{AB}{A^{\prime }{B}^{\prime }}}={\displaystyle \frac{OA}{O{A}^{\prime }}}\left(1\right)$

+ $\mathrm{\Delta }{F}^{\prime }OI\text{~}\mathrm{\Delta }{F}^{\prime }{A}^{\prime }{B}^{\prime }\Rightarrow {\displaystyle \frac{O{F}^{\prime }}{A^{\prime }{F}^{\prime }}}={\displaystyle \frac{OI}{A^{\prime }{B}^{\prime }}}\left(2\right)$

Lại có: $OI=AB$

$\begin{array}{l}\Rightarrow {\displaystyle \frac{OA}{O{A}^{\prime }}}={\displaystyle \frac{{\mathrm{O}\mathrm{F}}^{\prime }}{A{F}^{\prime }}}\Rightarrow {\displaystyle \frac{O{A}^{\prime }}{OA}}={\displaystyle \frac{A{F}^{\prime }}{O{F}^{\prime }}}={\displaystyle \frac{O{A}^{\prime }+{\mathrm{O}\mathrm{F}}^{\prime }}{{\mathrm{O}\mathrm{F}}^{\prime }}}={\displaystyle \frac{O{A}^{\prime }}{{\mathrm{O}\mathrm{F}}^{\prime }}}+1\\ \iff {\displaystyle \frac{O{A}^{\prime }}{OA}}={\displaystyle \frac{O{A}^{\prime }}{O{F}^{\prime }}}+{\displaystyle \frac{O{A}^{\prime }}{O{A}^{\prime }}}\\ \Rightarrow {\displaystyle \frac{1}{OA}}={\displaystyle \frac{1}{O{F}^{\prime }}}+{\displaystyle \frac{1}{O{A}^{\prime }}}\\ \Rightarrow {\displaystyle \frac{1}{O{F}^{\prime }}}={\displaystyle \frac{1}{OA}}–{\displaystyle \frac{1}{O{A}^{\prime }}}\end{array}$

Hay ${\displaystyle \frac{1}{f}}={\displaystyle \frac{1}{d}}–{\displaystyle \frac{1}{d^{\prime }}}$  (ĐPCM)

XÉT VỚI THẤU KÍNH PHÂN KÌ

Ta có:

+ $\mathrm{\Delta }OAB\text{~}\mathrm{\Delta }O{A}^{\prime }{B}^{\prime }\Rightarrow {\displaystyle \frac{AB}{A^{\prime }{B}^{\prime }}}={\displaystyle \frac{OA}{O{A}^{\prime }}}\left(1\right)$

+ $\mathrm{\Delta }I\mathrm{O}{\mathrm{F}}^{\prime }\text{~}\mathrm{\Delta }{\mathrm{B}}^{\prime }{\mathrm{A}}^{\prime }{\mathrm{F}}^{\prime }\Rightarrow {\displaystyle \frac{IO}{B^{\prime }{A}^{\prime }}}={\displaystyle \frac{\mathrm{O}{F}^{\prime }}{A^{\prime }{F}^{\prime }}}\left(2\right)$

Mà $IO=AB$

Từ (1) và (2) ta suy ra:

$\begin{array}{l}{\displaystyle \frac{OA}{O{A}^{\prime }}}={\displaystyle \frac{O{\mathrm{F}}^{\prime }}{A^{\prime }{F}^{\prime }}}\\ \Rightarrow {\displaystyle \frac{O{A}^{\prime }}{OA}}={\displaystyle \frac{A^{\prime }{F}^{\prime }}{{\mathrm{O}\mathrm{F}}^{\prime }}}={\displaystyle \frac{{\mathrm{O}\mathrm{F}}^{\prime }–O{A}^{\prime }}{O{F}^{\prime }}}=1–{\displaystyle \frac{O{A}^{\prime }}{O{F}^{\prime }}}\\ \iff {\displaystyle \frac{O{A}^{\prime }}{OA}}={\displaystyle \frac{O{A}^{\prime }}{O{A}^{\prime }}}–{\displaystyle \frac{O{A}^{\prime }}{O{F}^{\prime }}}\\ \Rightarrow {\displaystyle \frac{1}{OA}}={\displaystyle \frac{1}{O{A}^{\prime }}}–{\displaystyle \frac{1}{O{F}^{\prime }}}\\ \Rightarrow {\displaystyle \frac{1}{O{F}^{\prime }}}={\displaystyle \frac{1}{O{A}^{\prime }}}–{\displaystyle \frac{1}{OA}}\end{array}$

Hay ${\displaystyle \frac{1}{f}}={\displaystyle \frac{1}{d^{\prime }}}–{\displaystyle \frac{1}{d}}$ (ĐPCM)

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